LMFDB - Embedded newform 18.6.c.b.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,6,Mod(7,18)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("18.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	18.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.88690875663$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.47347183152.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 118x^{4} - 231x^{3} + 3700x^{2} - 3585x + 32331 $ x^6 - 3x^5 + 118x^4 - 231x^3 + 3700x^2 - 3585*x + 32331
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			13.2
Root			$0.500000 - 8.40123i$ of defining polynomial
Character	$\chi$	$=$	18.13
Dual form			18.6.c.b.7.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.00000 - 3.46410i) q^{2} +(-2.43381 + 15.3973i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-20.8014 + 36.0292i) q^{5} +(58.2054 - 22.3636i) q^{6} +(101.661 + 176.082i) q^{7} +64.0000 q^{8} +(-231.153 - 74.9483i) q^{9} +166.412 q^{10} +(-235.168 - 407.323i) q^{11} +(-193.881 - 156.902i) q^{12} +(-241.506 + 418.300i) q^{13} +(406.643 - 704.326i) q^{14} +(-504.125 - 407.974i) q^{15} +(-128.000 - 221.703i) q^{16} +1259.86 q^{17} +(202.678 + 950.634i) q^{18} +1978.94 q^{19} +(-332.823 - 576.466i) q^{20} +(-2958.60 + 1136.75i) q^{21} +(-940.672 + 1629.29i) q^{22} +(-239.119 + 414.166i) q^{23} +(-155.764 + 985.427i) q^{24} +(697.100 + 1207.41i) q^{25} +1932.04 q^{26} +(1716.58 - 3376.72i) q^{27} -3253.14 q^{28} +(580.249 + 1005.02i) q^{29} +(-405.015 + 2562.29i) q^{30} +(1186.50 - 2055.07i) q^{31} +(-512.000 + 886.810i) q^{32} +(6844.02 - 2629.60i) q^{33} +(-2519.72 - 4364.28i) q^{34} -8458.76 q^{35} +(2887.74 - 2603.37i) q^{36} +8185.10 q^{37} +(-3957.89 - 6855.26i) q^{38} +(-5852.91 - 4736.60i) q^{39} +(-1331.29 + 2305.87i) q^{40} +(-8758.87 + 15170.8i) q^{41} +(9855.02 + 7975.40i) q^{42} +(-11435.0 - 19806.1i) q^{43} +7525.37 q^{44} +(7508.64 - 6769.22i) q^{45} +1912.95 q^{46} +(8685.43 + 15043.6i) q^{47} +(3725.15 - 1431.27i) q^{48} +(-12266.3 + 21245.9i) q^{49} +(2788.40 - 4829.65i) q^{50} +(-3066.26 + 19398.4i) q^{51} +(-3864.09 - 6692.80i) q^{52} -5390.58 q^{53} +(-15130.5 + 807.021i) q^{54} +19567.3 q^{55} +(6506.29 + 11269.2i) q^{56} +(-4816.38 + 30470.4i) q^{57} +(2321.00 - 4020.09i) q^{58} +(22281.8 - 38593.2i) q^{59} +(9686.05 - 3721.56i) q^{60} +(-2084.17 - 3609.88i) q^{61} -9491.97 q^{62} +(-10302.2 - 48321.1i) q^{63} +4096.00 q^{64} +(-10047.3 - 17402.5i) q^{65} +(-22797.3 - 18449.2i) q^{66} +(-1228.46 + 2127.76i) q^{67} +(-10078.9 + 17457.1i) q^{68} +(-5795.07 - 4689.79i) q^{69} +(16917.5 + 29302.0i) q^{70} +2184.37 q^{71} +(-14793.8 - 4796.69i) q^{72} +3037.34 q^{73} +(-16370.2 - 28354.0i) q^{74} +(-20287.5 + 7794.83i) q^{75} +(-15831.5 + 27421.0i) q^{76} +(47814.7 - 82817.5i) q^{77} +(-4702.24 + 29748.3i) q^{78} +(25266.2 + 43762.3i) q^{79} +10650.3 q^{80} +(47814.5 + 34649.1i) q^{81} +70070.9 q^{82} +(25913.9 + 44884.2i) q^{83} +(7917.55 - 50089.6i) q^{84} +(-26206.9 + 45391.7i) q^{85} +(-45740.1 + 79224.3i) q^{86} +(-16886.8 + 6488.23i) q^{87} +(-15050.7 - 26068.7i) q^{88} -20154.7 q^{89} +(-38466.5 - 12472.3i) q^{90} -98206.5 q^{91} +(-3825.91 - 6626.66i) q^{92} +(28754.8 + 23270.5i) q^{93} +(34741.7 - 60174.4i) q^{94} +(-41164.9 + 71299.6i) q^{95} +(-12408.4 - 10041.7i) q^{96} +(-40214.4 - 69653.3i) q^{97} +98130.4 q^{98} +(23831.7 + 111779. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 12 q^{2} + 9 q^{3} - 48 q^{4} - 54 q^{5} - 12 q^{6} - 132 q^{7} + 384 q^{8} - 177 q^{9} + 432 q^{10} - 315 q^{11} - 96 q^{12} - 744 q^{13} - 528 q^{14} + 2286 q^{15} - 768 q^{16} + 2898 q^{17} + 1056 q^{18}+ \cdots + 282168 q^{99}+O(q^{100}) $ 6 * q - 12 * q^2 + 9 * q^3 - 48 * q^4 - 54 * q^5 - 12 * q^6 - 132 * q^7 + 384 * q^8 - 177 * q^9 + 432 * q^10 - 315 * q^11 - 96 * q^12 - 744 * q^13 - 528 * q^14 + 2286 * q^15 - 768 * q^16 + 2898 * q^17 + 1056 * q^18 + 2262 * q^19 - 864 * q^20 - 11076 * q^21 - 1260 * q^22 - 3168 * q^23 + 576 * q^24 - 2883 * q^25 + 5952 * q^26 + 18144 * q^27 + 4224 * q^28 - 5148 * q^29 - 14400 * q^30 - 8610 * q^31 - 3072 * q^32 + 17469 * q^33 - 5796 * q^34 + 2700 * q^35 - 1392 * q^36 + 39936 * q^37 - 4524 * q^38 - 49026 * q^39 - 3456 * q^40 + 5049 * q^41 + 41352 * q^42 - 31389 * q^43 + 10080 * q^44 + 2538 * q^45 + 25344 * q^46 + 12924 * q^47 - 768 * q^48 - 52857 * q^49 - 11532 * q^50 + 36837 * q^51 - 11904 * q^52 - 96048 * q^53 - 71892 * q^54 + 126252 * q^55 - 8448 * q^56 - 17469 * q^57 - 20592 * q^58 + 62955 * q^59 + 21024 * q^60 - 75966 * q^61 + 68880 * q^62 + 49578 * q^63 + 24576 * q^64 + 108702 * q^65 + 2952 * q^66 - 32991 * q^67 - 23184 * q^68 - 29250 * q^69 - 5400 * q^70 - 129672 * q^71 - 11328 * q^72 - 8466 * q^73 - 79872 * q^74 - 105483 * q^75 - 18096 * q^76 + 88740 * q^77 + 171720 * q^78 + 89202 * q^79 + 27648 * q^80 + 123435 * q^81 - 40392 * q^82 + 32634 * q^83 + 11808 * q^84 + 71388 * q^85 - 125556 * q^86 - 151524 * q^87 - 20160 * q^88 + 66132 * q^89 - 263088 * q^90 - 301836 * q^91 - 50688 * q^92 + 57678 * q^93 + 51696 * q^94 - 82944 * q^95 - 6144 * q^96 + 46245 * q^97 + 422856 * q^98 + 282168 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$2$	−2.00000	−	3.46410i	−0.353553	−	0.612372i
$3$	−2.43381	+	15.3973i	−0.156129	+	0.987737i
$3$	−2.43381	+	15.3973i	−0.156129	+	0.987737i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−20.8014	+	36.0292i	−0.372108	+	0.644509i	−0.989890	−	0.141840i	$-0.954698\pi$
$5$	−20.8014	+	36.0292i	−0.372108	+	0.644509i	0.617782	+	0.786349i	$0.288031\pi$
$6$	58.2054	−	22.3636i	0.660063	−	0.253608i
$7$	101.661	+	176.082i	0.784166	+	1.35822i	0.929496	+	0.368832i	$0.120242\pi$
$7$	101.661	+	176.082i	0.784166	+	1.35822i	−0.145330	+	0.989383i	$0.546424\pi$
$8$	64.0000			0.353553
$9$	−231.153	−	74.9483i	−0.951247	−	0.308429i
$10$	166.412			0.526239
$11$	−235.168	−	407.323i	−0.585998	−	1.01498i	−0.994750	−	0.102333i	$-0.967369\pi$
$11$	−235.168	−	407.323i	−0.585998	−	1.01498i	0.408752	−	0.912646i	$-0.365964\pi$
$12$	−193.881	−	156.902i	−0.388670	−	0.314540i
$13$	−241.506	+	418.300i	−0.396341	+	0.686482i	−0.993271	−	0.115811i	$-0.963053\pi$
$13$	−241.506	+	418.300i	−0.396341	+	0.686482i	0.596931	+	0.802293i	$0.296387\pi$
$14$	406.643	−	704.326i	0.554489	−	0.960403i
$15$	−504.125	−	407.974i	−0.578508	−	0.468171i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	1259.86			1.05730			0.528652	−	0.848839i	$-0.322698\pi$
$17$	1259.86			1.05730			0.528652	+	0.848839i	$0.322698\pi$
$18$	202.678	+	950.634i	0.147443	+	0.691564i
$19$	1978.94			1.25762			0.628810	−	0.777559i	$-0.283542\pi$
$19$	1978.94			1.25762			0.628810	+	0.777559i	$0.283542\pi$
$20$	−332.823	−	576.466i	−0.186054	−	0.322255i
$21$	−2958.60	+	1136.75i	−1.46399	+	0.562492i
$22$	−940.672	+	1629.29i	−0.414363	+	0.717698i
$23$	−239.119	+	414.166i	−0.0942529	+	0.163251i	−0.909297	−	0.416149i	$-0.863380\pi$
$23$	−239.119	+	414.166i	−0.0942529	+	0.163251i	0.815044	+	0.579400i	$0.196713\pi$
$24$	−155.764	+	985.427i	−0.0552000	+	0.349218i
$25$	697.100	+	1207.41i	0.223072	+	0.386372i
$26$	1932.04			0.560511
$27$	1716.58	−	3376.72i	0.453164	−	0.891427i
$28$	−3253.14			−0.784166
$29$	580.249	+	1005.02i	0.128121	+	0.221912i	0.922949	−	0.384923i	$-0.125772\pi$
$29$	580.249	+	1005.02i	0.128121	+	0.221912i	−0.794828	+	0.606835i	$0.792439\pi$
$30$	−405.015	+	2562.29i	−0.0821614	+	0.519786i
$31$	1186.50	−	2055.07i	0.221749	−	0.384081i	−0.733590	−	0.679592i	$-0.762157\pi$
$31$	1186.50	−	2055.07i	0.221749	−	0.384081i	0.955339	+	0.295511i	$0.0954901\pi$
$32$	−512.000	+	886.810i	−0.0883883	+	0.153093i
$33$	6844.02	−	2629.60i	1.09402	−	0.420344i
$34$	−2519.72	−	4364.28i	−0.373813	−	0.647464i
$35$	−8458.76			−1.16718
$36$	2887.74	−	2603.37i	0.371366	−	0.334795i
$37$	8185.10			0.982923			0.491462	−	0.870899i	$-0.336463\pi$
$37$	8185.10			0.982923			0.491462	+	0.870899i	$0.336463\pi$
$38$	−3957.89	−	6855.26i	−0.444636	−	0.770132i
$39$	−5852.91	−	4736.60i	−0.616183	−	0.498660i
$40$	−1331.29	+	2305.87i	−0.131560	+	0.227868i
$41$	−8758.87	+	15170.8i	−0.813745	+	1.40945i	0.0964809	+	0.995335i	$0.469241\pi$
$41$	−8758.87	+	15170.8i	−0.813745	+	1.40945i	−0.910226	+	0.414113i	$0.864092\pi$
$42$	9855.02	+	7975.40i	0.862054	+	0.697636i
$43$	−11435.0	−	19806.1i	−0.943119	−	1.63353i	−0.759475	−	0.650537i	$-0.774544\pi$
$43$	−11435.0	−	19806.1i	−0.943119	−	1.63353i	−0.183644	−	0.982993i	$-0.558789\pi$
$44$	7525.37			0.585998
$45$	7508.64	−	6769.22i	0.552752	−	0.498319i
$46$	1912.95			0.133294
$47$	8685.43	+	15043.6i	0.573518	+	0.993362i	0.996201	+	0.0870843i	$0.0277550\pi$
$47$	8685.43	+	15043.6i	0.573518	+	0.993362i	−0.422683	+	0.906277i	$0.638912\pi$
$48$	3725.15	−	1431.27i	0.233367	−	0.0896641i
$49$	−12266.3	+	21245.9i	−0.729833	+	1.26411i
$50$	2788.40	−	4829.65i	0.157736	−	0.273206i
$51$	−3066.26	+	19398.4i	−0.165076	+	1.04434i
$52$	−3864.09	−	6692.80i	−0.198170	−	0.343241i
$53$	−5390.58			−0.263600			−0.131800	−	0.991276i	$-0.542076\pi$
$53$	−5390.58			−0.263600			−0.131800	+	0.991276i	$0.542076\pi$
$54$	−15130.5	+	807.021i	−0.706103	+	0.0376617i
$55$	19567.3			0.872218
$56$	6506.29	+	11269.2i	0.277245	+	0.480202i
$57$	−4816.38	+	30470.4i	−0.196351	+	1.24220i
$58$	2321.00	−	4020.09i	0.0905951	−	0.156915i
$59$	22281.8	−	38593.2i	0.833335	−	1.44338i	−0.0620431	−	0.998073i	$-0.519762\pi$
$59$	22281.8	−	38593.2i	0.833335	−	1.44338i	0.895379	−	0.445306i	$-0.146905\pi$
$60$	9686.05	−	3721.56i	0.347351	−	0.133459i
$61$	−2084.17	−	3609.88i	−0.0717147	−	0.124213i	0.827938	−	0.560819i	$-0.189514\pi$
$61$	−2084.17	−	3609.88i	−0.0717147	−	0.124213i	−0.899653	+	0.436606i	$0.856180\pi$
$62$	−9491.97			−0.313601
$63$	−10302.2	−	48321.1i	−0.327023	−	1.53386i
$64$	4096.00			0.125000
$65$	−10047.3	−	17402.5i	−0.294963	−	0.510891i
$66$	−22797.3	−	18449.2i	−0.644203	−	0.521336i
$67$	−1228.46	+	2127.76i	−0.0334330	+	0.0579076i	−0.882258	−	0.470767i	$-0.843977\pi$
$67$	−1228.46	+	2127.76i	−0.0334330	+	0.0579076i	0.848825	+	0.528674i	$0.177311\pi$
$68$	−10078.9	+	17457.1i	−0.264326	+	0.457826i
$69$	−5795.07	−	4689.79i	−0.146533	−	0.118585i
$70$	16917.5	+	29302.0i	0.412659	+	0.714747i
$71$	2184.37			0.0514256			0.0257128	−	0.999669i	$-0.491814\pi$
$71$	2184.37			0.0514256			0.0257128	+	0.999669i	$0.491814\pi$
$72$	−14793.8	−	4796.69i	−0.336317	−	0.109046i
$73$	3037.34			0.0667093			0.0333546	−	0.999444i	$-0.489381\pi$
$73$	3037.34			0.0667093			0.0333546	+	0.999444i	$0.489381\pi$
$74$	−16370.2	−	28354.0i	−0.347516	−	0.601915i
$75$	−20287.5	+	7794.83i	−0.416462	+	0.160012i
$76$	−15831.5	+	27421.0i	−0.314405	+	0.544565i
$77$	47814.7	−	82817.5i	0.919040	−	1.59182i
$78$	−4702.24	+	29748.3i	−0.0875121	+	0.553637i
$79$	25266.2	+	43762.3i	0.455482	+	0.788918i	0.998716	−	0.0506633i	$-0.0161335\pi$
$79$	25266.2	+	43762.3i	0.455482	+	0.788918i	−0.543234	+	0.839582i	$0.682800\pi$
$80$	10650.3			0.186054
$81$	47814.5	+	34649.1i	0.809743	+	0.586785i
$82$	70070.9			1.15081
$83$	25913.9	+	44884.2i	0.412893	+	0.715152i	0.995205	−	0.0978135i	$-0.0311849\pi$
$83$	25913.9	+	44884.2i	0.412893	+	0.715152i	−0.582311	+	0.812966i	$0.697852\pi$
$84$	7917.55	−	50089.6i	0.122431	−	0.774550i
$85$	−26206.9	+	45391.7i	−0.393431	+	0.681442i
$86$	−45740.1	+	79224.3i	−0.666886	+	1.15508i
$87$	−16886.8	+	6488.23i	−0.239194	+	0.0919027i
$88$	−15050.7	−	26068.7i	−0.207182	−	0.358849i
$89$	−20154.7			−0.269713			−0.134857	−	0.990865i	$-0.543057\pi$
$89$	−20154.7			−0.269713			−0.134857	+	0.990865i	$0.543057\pi$
$90$	−38466.5	−	12472.3i	−0.500584	−	0.162308i
$91$	−98206.5			−1.24319
$92$	−3825.91	−	6626.66i	−0.0471264	−	0.0816254i
$93$	28754.8	+	23270.5i	0.344749	+	0.278996i
$94$	34741.7	−	60174.4i	0.405538	−	0.702413i
$95$	−41164.9	+	71299.6i	−0.467970	+	0.810547i
$96$	−12408.4	−	10041.7i	−0.137416	−	0.111207i
$97$	−40214.4	−	69653.3i	−0.433962	−	0.751644i	0.563248	−	0.826288i	$-0.309552\pi$
$97$	−40214.4	−	69653.3i	−0.433962	−	0.751644i	−0.997210	+	0.0746433i	$0.976218\pi$
$98$	98130.4			1.03214
$99$	23831.7	+	111779.i	0.244380	+	1.14623i
$100$	−22307.2			−0.223072
$101$	−28450.2	−	49277.2i	−0.277512	−	0.480665i	0.693254	−	0.720694i	$-0.256177\pi$
$101$	−28450.2	−	49277.2i	−0.277512	−	0.480665i	−0.970766	+	0.240028i	$0.922843\pi$
$102$	73330.7	−	28175.0i	0.697887	−	0.268141i
$103$	98505.0	−	170616.i	0.914882	−	1.58462i	0.107808	−	0.994172i	$-0.465617\pi$
$103$	98505.0	−	170616.i	0.914882	−	1.58462i	0.807074	−	0.590451i	$-0.201050\pi$
$104$	−15456.4	+	26771.2i	−0.140128	+	0.242708i
$105$	20587.0	−	130242.i	0.182230	−	1.15286i
$106$	10781.2	+	18673.5i	0.0931967	+	0.161421i
$107$	−23482.4			−0.198282			−0.0991411	−	0.995073i	$-0.531610\pi$
$107$	−23482.4			−0.198282			−0.0991411	+	0.995073i	$0.531610\pi$
$108$	33056.5	+	50799.5i	0.272708	+	0.419083i
$109$	−118550.			−0.955727			−0.477863	−	0.878434i	$-0.658589\pi$
$109$	−118550.			−0.955727			−0.477863	+	0.878434i	$0.658589\pi$
$110$	−39134.7	−	67783.2i	−0.308375	−	0.534122i
$111$	−19921.0	+	126028.i	−0.153463	+	0.970869i
$112$	26025.1	−	45076.9i	0.196042	−	0.339554i
$113$	223.401	−	386.942i	0.00164585	−	0.00285069i	−0.865201	−	0.501425i	$-0.832809\pi$
$113$	223.401	−	386.942i	0.00164585	−	0.00285069i	0.866847	+	0.498574i	$0.166143\pi$
$114$	115185.	−	44256.3i	0.830108	−	0.318943i
$115$	−9948.04	−	17230.5i	−0.0701444	−	0.121494i
$116$	−18568.0			−0.128121
$117$	87175.6	−	78590.9i	0.588749	−	0.530772i
$118$	−178254.			−1.17851
$119$	128078.	+	221838.i	0.829102	+	1.43605i
$120$	−32264.0	−	26110.3i	−0.204534	−	0.165523i
$121$	−30082.4	+	52104.3i	−0.186788	+	0.323527i
$122$	−8336.67	+	14439.5i	−0.0507099	+	0.0878322i
$123$	−212272.	−	171786.i	−1.26511	−	1.02382i
$124$	18983.9	+	32881.1i	0.110875	+	0.192040i
$125$	−188012.			−1.07624
$126$	−146785.	+	132330.i	−0.823673	+	0.742561i
$127$	193803.			1.06623			0.533116	−	0.846042i	$-0.321021\pi$
$127$	193803.			1.06623			0.533116	+	0.846042i	$0.321021\pi$
$128$	−8192.00	−	14189.0i	−0.0441942	−	0.0765466i
$129$	332790.	−	127864.i	1.76075	−	0.676511i
$130$	−40189.3	+	69609.9i	−0.208570	+	0.361254i
$131$	−48037.8	+	83203.8i	−0.244571	+	0.423609i	−0.962011	−	0.273011i	$-0.911980\pi$
$131$	−48037.8	+	83203.8i	−0.244571	+	0.423609i	0.717440	+	0.696620i	$0.245314\pi$
$132$	−18315.4	+	115870.i	−0.0914915	+	0.578812i
$133$	201181.	+	348455.i	0.986183	+	1.70812i
$134$	9827.70			0.0472813
$135$	85953.0	+	132088.i	0.405907	+	0.623775i
$136$	80631.0			0.373813
$137$	−116089.	−	201071.i	−0.528431	−	0.915269i	−0.999451	−	0.0331465i	$-0.989447\pi$
$137$	−116089.	−	201071.i	−0.528431	−	0.915269i	0.471020	−	0.882123i	$-0.343886\pi$
$138$	−4655.77	+	29454.3i	−0.0208110	+	0.131659i
$139$	80284.0	−	139056.i	0.352445	−	0.610453i	−0.634232	−	0.773143i	$-0.718684\pi$
$139$	80284.0	−	139056.i	0.352445	−	0.610453i	0.986677	+	0.162689i	$0.0520169\pi$
$140$	67670.1	−	117208.i	0.291794	−	0.505402i
$141$	−252770.	+	97118.8i	−1.07072	+	0.411392i
$142$	−4368.73	−	7566.87i	−0.0181817	−	0.0314916i
$143$	227177.			0.929020
$144$	12971.4	+	60840.6i	0.0521290	+	0.244505i
$145$	−48280.1			−0.190699
$146$	−6074.68	−	10521.7i	−0.0235853	−	0.0408509i
$147$	−297275.	−	240576.i	−1.13466	−	0.918247i
$148$	−65480.8	+	113416.i	−0.245731	+	0.425618i
$149$	139592.	−	241781.i	0.515105	−	0.892189i	−0.484741	−	0.874658i	$-0.661086\pi$
$149$	139592.	−	241781.i	0.515105	−	0.892189i	0.999846	−	0.0175309i	$-0.00558055\pi$
$150$	67577.1	+	54688.3i	0.245229	+	0.198457i
$151$	14288.8	+	24749.0i	0.0509981	+	0.0883314i	0.890398	−	0.455184i	$-0.150426\pi$
$151$	14288.8	+	24749.0i	0.0509981	+	0.0883314i	−0.839399	+	0.543515i	$0.817093\pi$
$152$	126652.			0.444636
$153$	−291221.	−	94424.3i	−1.00576	−	0.326103i
$154$	−382517.			−1.29972
$155$	49361.6	+	85496.9i	0.165029	+	0.285839i
$156$	112455.	−	43207.5i	0.369972	−	0.142150i
$157$	62127.0	−	107607.i	0.201155	−	0.348411i	−0.747746	−	0.663985i	$-0.768864\pi$
$157$	62127.0	−	107607.i	0.201155	−	0.348411i	0.948901	+	0.315574i	$0.102197\pi$
$158$	101065.	−	175049.i	0.322075	−	0.557850i
$159$	13119.7	−	83000.3i	0.0411557	−	0.260367i
$160$	−21300.7	−	36893.9i	−0.0657799	−	0.113934i
$161$	−97236.1			−0.295640
$162$	24398.8	−	234932.i	0.0730435	−	0.703324i
$163$	163892.			0.483159			0.241579	−	0.970381i	$-0.422335\pi$
$163$	163892.			0.483159			0.241579	+	0.970381i	$0.422335\pi$
$164$	−140142.	−	242733.i	−0.406872	−	0.704724i
$165$	−47623.2	+	301284.i	−0.136179	+	0.861521i
$166$	103656.	−	179537.i	0.291960	−	0.505689i
$167$	81164.7	−	140581.i	0.225204	−	0.390065i	−0.731177	−	0.682188i	$-0.761028\pi$
$167$	81164.7	−	140581.i	0.225204	−	0.390065i	0.956381	+	0.292123i	$0.0943618\pi$
$168$	−189351.	+	72752.0i	−0.517599	+	0.198871i
$169$	68996.6	+	119506.i	0.185828	+	0.321863i
$170$	209655.			0.556395
$171$	−457439.	−	148318.i	−1.19631	−	0.387887i
$172$	365921.			0.943119
$173$	192179.	+	332863.i	0.488191	+	0.845572i	0.999908	−	0.0135821i	$-0.00432345\pi$
$173$	192179.	+	332863.i	0.488191	+	0.845572i	−0.511716	+	0.859154i	$0.670990\pi$
$174$	56249.6	+	45521.2i	0.140846	+	0.113983i
$175$	−141735.	+	245493.i	−0.349851	+	0.605960i
$176$	−60203.0	+	104275.i	−0.146500	+	0.253745i
$177$	540001.	+	437008.i	1.29557	+	1.04847i
$178$	40309.5	+	69818.1i	0.0953581	+	0.165165i
$179$	−511991.			−1.19434			−0.597172	−	0.802113i	$-0.703709\pi$
$179$	−511991.			−1.19434			−0.597172	+	0.802113i	$0.703709\pi$
$180$	33727.9	+	158197.i	0.0775904	+	0.363928i
$181$	−285832.			−0.648507			−0.324254	−	0.945970i	$-0.605113\pi$
$181$	−285832.			−0.648507			−0.324254	+	0.945970i	$0.605113\pi$
$182$	196413.	+	340197.i	0.439533	+	0.761294i
$183$	60654.9	−	23304.7i	0.133887	−	0.0514419i
$184$	−15303.6	+	26506.7i	−0.0333234	+	0.0577179i
$185$	−170262.	+	294902.i	−0.365753	+	0.633503i
$186$	23101.7	−	146151.i	0.0489622	−	0.309755i
$187$	−296279.	−	513170.i	−0.619578	−	1.07314i
$188$	−277934.			−0.573518
$189$	769087.	−	41021.1i	1.56611	−	0.0835321i
$190$	329319.			0.661809
$191$	−18626.1	−	32261.4i	−0.0369436	−	0.0639882i	0.846962	−	0.531653i	$-0.178429\pi$
$191$	−18626.1	−	32261.4i	−0.0369436	−	0.0639882i	−0.883906	+	0.467665i	$0.845096\pi$
$192$	−9968.90	+	63067.3i	−0.0195162	+	0.123467i
$193$	−289378.	+	501217.i	−0.559206	+	0.968573i	0.438357	+	0.898801i	$0.355561\pi$
$193$	−289378.	+	501217.i	−0.559206	+	0.968573i	−0.997563	+	0.0697722i	$0.977773\pi$
$194$	−160857.	+	278613.i	−0.306858	+	0.531493i
$195$	292404.	−	112347.i	0.550678	−	0.211581i
$196$	−196261.	−	339934.i	−0.364917	−	0.632054i
$197$	234386.			0.430294			0.215147	−	0.976582i	$-0.430977\pi$
$197$	234386.			0.430294			0.215147	+	0.976582i	$0.430977\pi$
$198$	339552.	−	306114.i	0.615521	−	0.554907i
$199$	200551.			0.358997			0.179499	−	0.983758i	$-0.442552\pi$
$199$	200551.			0.358997			0.179499	+	0.983758i	$0.442552\pi$
$200$	44614.4	+	77274.4i	0.0788679	+	0.136603i
$201$	−29771.9	−	24093.6i	−0.0519776	−	0.0420640i
$202$	−113801.	+	197109.i	−0.196231	+	0.339882i
$203$	−117977.	+	204342.i	−0.200936	+	0.348031i
$204$	−244262.	−	197675.i	−0.410943	−	0.332565i
$205$	−364394.	−	631149.i	−0.605601	−	1.04893i
$206$	−788040.			−1.29384
$207$	86314.2	−	77814.3i	0.140009	−	0.126222i
$208$	123651.			0.198170
$209$	−465384.	−	806069.i	−0.736963	−	1.27646i
$210$	−492345.	+	189168.i	−0.770410	+	0.296006i
$211$	269826.	−	467352.i	0.417232	−	0.722667i	−0.578428	−	0.815733i	$-0.696334\pi$
$211$	269826.	−	467352.i	0.417232	−	0.722667i	0.995660	+	0.0930667i	$0.0296670\pi$
$212$	43124.6	−	74694.0i	0.0659000	−	0.114142i
$213$	−5316.34	+	33633.3i	−0.00802905	+	0.0507950i
$214$	46964.9	+	81345.5i	0.0701033	+	0.121423i
$215$	951461.			1.40377
$216$	109861.	−	216110.i	0.160218	−	0.315167i
$217$	482480.			0.695553
$218$	237099.	+	410668.i	0.337900	+	0.585261i
$219$	−7392.32	+	46766.8i	−0.0104153	+	0.0658912i
$220$	−156539.	+	271133.i	−0.218054	+	0.377681i
$221$	−304263.	+	526999.i	−0.419053	+	0.725821i
$222$	476417.	−	183048.i	0.648791	−	0.249278i
$223$	−442584.	−	766578.i	−0.595983	−	1.03227i	−0.993407	−	0.114638i	$-0.963429\pi$
$223$	−442584.	−	766578.i	−0.595983	−	1.03227i	0.397424	−	0.917635i	$-0.369904\pi$
$224$	−208201.			−0.277245
$225$	−70643.3	−	331344.i	−0.0930282	−	0.436337i
$226$	−1787.21			−0.00232758
$227$	−159067.	−	275512.i	−0.204887	−	0.354875i	0.745210	−	0.666830i	$-0.232349\pi$
$227$	−159067.	−	275512.i	−0.204887	−	0.354875i	−0.950097	+	0.311955i	$0.899016\pi$
$228$	−383679.	−	310501.i	−0.488799	−	0.395572i
$229$	−246934.	+	427703.i	−0.311166	+	0.538956i	−0.978615	−	0.205700i	$-0.934053\pi$
$229$	−246934.	+	427703.i	−0.311166	+	0.538956i	0.667449	+	0.744656i	$0.267386\pi$
$230$	−39792.2	+	68922.1i	−0.0495996	+	0.0859090i
$231$	1.15879e6	+	937779.i	1.42881	+	1.15630i
$232$	37136.0	+	64321.4i	0.0452976	+	0.0784577i
$233$	1.16189e6			1.40208			0.701041	−	0.713121i	$-0.252719\pi$
$233$	1.16189e6			1.40208			0.701041	+	0.713121i	$0.252719\pi$
$234$	−446598.	−	144803.i	−0.533184	−	0.172878i
$235$	−722678.			−0.853641
$236$	356508.	+	617491.i	0.416668	+	0.721690i
$237$	−735313.	+	282521.i	−0.850358	+	0.326723i
$238$	512313.	−	887352.i	0.586264	−	1.01544i
$239$	579263.	−	1.00331e6i	0.655965	−	1.13617i	−0.325685	−	0.945478i	$-0.605595\pi$
$239$	579263.	−	1.00331e6i	0.655965	−	1.13617i	0.981651	−	0.190687i	$-0.0610716\pi$
$240$	−25920.9	+	163986.i	−0.0290484	+	0.183772i
$241$	410557.	+	711106.i	0.455335	+	0.788663i	0.998707	−	0.0508285i	$-0.0161862\pi$
$241$	410557.	+	711106.i	0.455335	+	0.788663i	−0.543372	+	0.839492i	$0.682853\pi$
$242$	240659.			0.264158
$243$	−649873.	+	651885.i	−0.706013	+	0.708198i
$244$	66693.4			0.0717147
$245$	−510314.	−	883889.i	−0.543153	−	0.940768i
$246$	−170540.	+	1.07890e6i	−0.179675	+	1.13670i
$247$	−477926.	+	827792.i	−0.498446	+	0.863334i
$248$	75935.7	−	131525.i	0.0784002	−	0.135793i
$249$	−754165.	+	289764.i	−0.770847	+	0.296174i
$250$	376024.	+	651292.i	0.380509	+	0.659061i
$251$	−852357.			−0.853959			−0.426980	−	0.904261i	$-0.640422\pi$
$251$	−852357.			−0.853959			−0.426980	+	0.904261i	$0.640422\pi$
$252$	751974.	+	243817.i	0.745936	+	0.241860i
$253$	224933.			0.220928
$254$	−387606.	−	671354.i	−0.376970	−	0.652931i
$255$	−635126.	−	513990.i	−0.611659	−	0.494999i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−650171.	+	1.12613e6i	−0.614037	+	1.06354i	0.376515	+	0.926410i	$0.377122\pi$
$257$	−650171.	+	1.12613e6i	−0.614037	+	1.06354i	−0.990553	+	0.137133i	$0.956211\pi$
$258$	−1.10852e6	−	897091.i	−1.03679	−	0.839049i
$259$	832103.	+	1.44124e6i	0.770775	+	1.33502i
$260$	321515.			0.294963
$261$	−58801.8	−	275803.i	−0.0534305	−	0.250609i
$262$	384302.			0.345875
$263$	572288.	+	991232.i	0.510182	+	0.883662i	0.999930	+	0.0117977i	$0.00375542\pi$
$263$	572288.	+	991232.i	0.510182	+	0.883662i	−0.489748	+	0.871864i	$0.662911\pi$
$264$	438017.	−	168294.i	0.386796	−	0.148614i
$265$	112132.	−	194218.i	0.0980876	−	0.169893i
$266$	804723.	−	1.39382e6i	0.697336	−	1.20782i
$267$	49052.9	−	310329.i	0.0421101	−	0.266406i
$268$	−19655.4	−	34044.1i	−0.0167165	−	0.0289538i
$269$	1.54095e6			1.29840			0.649199	−	0.760619i	$-0.275104\pi$
$269$	1.54095e6			1.29840			0.649199	+	0.760619i	$0.275104\pi$
$270$	285659.	−	561925.i	0.238473	−	0.469104i
$271$	1.42397e6			1.17782			0.588908	−	0.808200i	$-0.299558\pi$
$271$	1.42397e6			1.17782			0.588908	+	0.808200i	$0.299558\pi$
$272$	−161262.	−	279314.i	−0.132163	−	0.228913i
$273$	239016.	−	1.51211e6i	0.194098	−	1.22794i
$274$	−464355.	+	804286.i	−0.373657	+	0.647193i
$275$	327871.	−	567889.i	0.261440	−	0.452827i
$276$	111344.	−	42780.5i	0.0879822	−	0.0338044i
$277$	−798009.	−	1.38219e6i	−0.624897	−	1.08235i	−0.988561	−	0.150823i	$-0.951808\pi$
$277$	−798009.	−	1.38219e6i	−0.624897	−	1.08235i	0.363664	−	0.931530i	$-0.381526\pi$
$278$	−642272.			−0.498433
$279$	−428286.	+	386110.i	−0.329400	+	0.296962i
$280$	−541361.			−0.412659
$281$	−200767.	−	347738.i	−0.151679	−	0.262716i	0.780166	−	0.625573i	$-0.215135\pi$
$281$	−200767.	−	347738.i	−0.151679	−	0.262716i	−0.931845	+	0.362857i	$0.881801\pi$
$282$	841968.	+	681382.i	0.630483	+	0.510232i
$283$	−535582.	+	927656.i	−0.397521	+	0.688527i	−0.993419	−	0.114533i	$-0.963463\pi$
$283$	−535582.	+	927656.i	−0.397521	+	0.688527i	0.595898	+	0.803060i	$0.296796\pi$
$284$	−17474.9	+	30267.5i	−0.0128564	+	0.0222680i
$285$	−997634.	−	807358.i	−0.727544	−	0.588781i
$286$	−454355.	−	786966.i	−0.328458	−	0.568906i
$287$	−3.56173e6			−2.55244
$288$	184815.	−	166615.i	0.131298	−	0.118368i
$289$	167390.			0.117892
$290$	96560.2	+	167247.i	0.0674222	+	0.116779i
$291$	1.17035e6	−	449669.i	0.810181	−	0.311287i
$292$	−24298.7	+	42086.6i	−0.0166773	+	0.0288860i
$293$	358830.	−	621511.i	0.244185	−	0.422941i	−0.717717	−	0.696335i	$-0.754813\pi$
$293$	358830.	−	621511.i	0.244185	−	0.422941i	0.961902	+	0.273394i	$0.0881462\pi$
$294$	−238831.	+	1.51094e6i	−0.161147	+	1.01948i
$295$	926986.	+	1.60559e6i	0.620181	+	1.07418i
$296$	523846.			0.347516
$297$	−1.77910e6	+	94892.7i	−1.17033	+	0.0624226i
$298$	−1.11674e6			−0.728469
$299$	−115497.	−	200047.i	−0.0747125	−	0.129406i
$300$	54291.6	−	343470.i	0.0348281	−	0.220336i
$301$	2.32499e6	−	4.02700e6i	1.47912	−	2.56192i
$302$	57155.3	−	98995.9i	0.0360611	−	0.0624597i
$303$	827978.	−	318125.i	0.518098	−	0.199063i
$304$	−253305.	−	438737.i	−0.157202	−	0.272283i
$305$	173415.			0.106742
$306$	255346.	+	1.19767e6i	0.155892	+	0.731193i
$307$	−2.25621e6			−1.36626			−0.683131	−	0.730296i	$-0.739382\pi$
$307$	−2.25621e6			−1.36626			−0.683131	+	0.730296i	$0.739382\pi$
$308$	765035.	+	1.32508e6i	0.459520	+	0.795912i
$309$	2.38728e6	+	1.93196e6i	1.42235	+	1.15107i
$310$	197447.	−	341988.i	0.116693	−	0.202118i
$311$	−897190.	+	1.55398e6i	−0.525997	+	0.911054i	0.473544	+	0.880770i	$0.342974\pi$
$311$	−897190.	+	1.55398e6i	−0.525997	+	0.911054i	−0.999541	+	0.0302837i	$0.990359\pi$
$312$	−374586.	−	303142.i	−0.217854	−	0.176303i
$313$	281895.	+	488257.i	0.162640	+	0.281701i	0.935815	−	0.352492i	$-0.114666\pi$
$313$	281895.	+	488257.i	0.162640	+	0.281701i	−0.773175	+	0.634193i	$0.781332\pi$
$314$	−497016.			−0.284476
$315$	1.95527e6	+	633969.i	1.11027	+	0.359991i
$316$	−808517.			−0.455482
$317$	1.59153e6	+	2.75662e6i	0.889544	+	1.54074i	0.840415	+	0.541943i	$0.182311\pi$
$317$	1.59153e6	+	2.75662e6i	0.889544	+	1.54074i	0.0491288	+	0.998792i	$0.484356\pi$
$318$	−313761.	+	120553.i	−0.173993	+	0.0668512i
$319$	272912.	−	472698.i	0.150157	−	0.260080i
$320$	−85202.7	+	147575.i	−0.0465134	+	0.0805636i
$321$	57151.9	−	361566.i	0.0309576	−	0.195851i
$322$	194472.	+	336836.i	0.104524	+	0.181042i
$323$	2.49319e6			1.32969
$324$	−862627.	+	385345.i	−0.456521	+	0.203933i
$325$	−673414.			−0.353650
$326$	−327785.	−	567740.i	−0.170822	−	0.295873i
$327$	288528.	−	1.82534e6i	0.149217	−	0.944006i
$328$	−560567.	+	970931.i	−0.287702	+	0.498315i
$329$	−1.76593e6	+	3.05869e6i	−0.899466	+	1.55792i
$330$	1.13892e6	−	437596.i	0.575718	−	0.221202i
$331$	3762.47	+	6516.79i	0.00188757	+	0.00326937i	0.866968	−	0.498364i	$-0.166066\pi$
$331$	3762.47	+	6516.79i	0.00188757	+	0.00326937i	−0.865080	+	0.501634i	$0.832733\pi$
$332$	−829246.			−0.412893
$333$	−1.89201e6	−	613459.i	−0.935003	−	0.303162i
$334$	−649318.			−0.318487
$335$	−51107.6	−	88520.9i	−0.0248813	−	0.0430957i
$336$	630721.	+	510425.i	0.304782	+	0.246652i
$337$	734831.	−	1.27277e6i	0.352463	−	0.610483i	−0.634218	−	0.773154i	$-0.718678\pi$
$337$	734831.	−	1.27277e6i	0.352463	−	0.610483i	0.986680	+	0.162671i	$0.0520111\pi$
$338$	275986.	−	478023.i	0.131400	−	0.227592i
$339$	5414.14	+	4381.51i	0.00255876	+	0.00207074i
$340$	−419310.	−	726267.i	−0.196715	−	0.340721i
$341$	−1.11610e6			−0.519779
$342$	401088.	+	1.88125e6i	0.185427	+	0.869724i
$343$	−1.57078e6			−0.720909
$344$	−731842.	−	1.26759e6i	−0.333443	−	0.577540i
$345$	289515.	−	111237.i	0.130955	−	0.0503155i
$346$	768715.	−	1.33145e6i	0.345203	−	0.597910i
$347$	1.31149e6	−	2.27156e6i	0.584709	−	1.01275i	−0.410203	−	0.911994i	$-0.634542\pi$
$347$	1.31149e6	−	2.27156e6i	0.584709	−	1.01275i	0.994912	−	0.100751i	$-0.0321246\pi$
$348$	45191.0	−	285897.i	0.0200034	−	0.126550i
$349$	−582327.	−	1.00862e6i	−0.255919	−	0.443265i	0.709225	−	0.704982i	$-0.249045\pi$
$349$	−582327.	−	1.00862e6i	−0.255919	−	0.443265i	−0.965145	+	0.261716i	$0.915711\pi$
$350$	1.13388e6			0.494764
$351$	997918.	+	1.53354e6i	0.432341	+	0.664398i
$352$	481624.			0.207182
$353$	−1.57339e6	−	2.72518e6i	−0.672045	−	1.16402i	−0.977323	−	0.211753i	$-0.932083\pi$
$353$	−1.57339e6	−	2.72518e6i	−0.672045	−	1.16402i	0.305278	−	0.952263i	$-0.401251\pi$
$354$	433838.	−	2.74463e6i	0.184001	−	1.16406i
$355$	−45438.0	+	78700.9i	−0.0191359	+	0.0331443i
$356$	161238.	−	279272.i	0.0674283	−	0.116789i
$357$	−3.72742e6	+	1.43215e6i	−1.54788	+	0.594726i
$358$	1.02398e6	+	1.77359e6i	0.422264	+	0.731383i
$359$	−720847.			−0.295194			−0.147597	−	0.989048i	$-0.547154\pi$
$359$	−720847.			−0.295194			−0.147597	+	0.989048i	$0.547154\pi$
$360$	480553.	−	433230.i	0.195427	−	0.176182i
$361$	1.44012e6			0.581607
$362$	571664.	+	990152.i	0.229282	+	0.397128i
$363$	−729050.	−	590000.i	−0.290396	−	0.235009i
$364$	785652.	−	1.36079e6i	0.310797	−	0.538316i
$365$	−63181.1	+	109433.i	−0.0248230	+	0.0429947i
$366$	−202040.	−	163505.i	−0.0788378	−	0.0638012i
$367$	−41258.2	−	71461.4i	−0.0159899	−	0.0276953i	0.857920	−	0.513784i	$-0.171757\pi$
$367$	−41258.2	−	71461.4i	−0.0159899	−	0.0276953i	−0.873910	+	0.486088i	$0.838423\pi$
$368$	122429.			0.0471264
$369$	3.16166e6	−	2.85032e6i	1.20879	−	1.08975i
$370$	1.36209e6			0.517253
$371$	−548010.	−	949181.i	−0.206706	−	0.358026i
$372$	−552484.	+	212275.i	−0.206996	+	0.0795318i
$373$	−2.65152e6	+	4.59256e6i	−0.986784	+	1.70916i	−0.353060	+	0.935601i	$0.614859\pi$
$373$	−2.65152e6	+	4.59256e6i	−0.986784	+	1.70916i	−0.633724	+	0.773560i	$0.718474\pi$
$374$	−1.18511e6	+	2.05268e6i	−0.438108	+	0.758826i
$375$	457586.	−	2.89487e6i	0.168033	−	1.06304i
$376$	555868.	+	962791.i	0.202769	+	0.351206i
$377$	−560534.			−0.203118
$378$	−1.68028e6	−	2.58215e6i	−0.604855	−	0.929507i
$379$	−49534.8			−0.0177138			−0.00885691	−	0.999961i	$-0.502819\pi$
$379$	−49534.8			−0.0177138			−0.00885691	+	0.999961i	$0.502819\pi$
$380$	−658638.	−	1.14079e6i	−0.233985	−	0.405274i
$381$	−471681.	+	2.98404e6i	−0.166470	+	1.05316i
$382$	−74504.6	+	129046.i	−0.0261231	+	0.0452465i
$383$	1.92179e6	−	3.32863e6i	0.669434	−	1.15949i	−0.308628	−	0.951183i	$-0.599870\pi$
$383$	1.92179e6	−	3.32863e6i	0.669434	−	1.15949i	0.978063	−	0.208311i	$-0.0667968\pi$
$384$	238409.	−	91601.3i	0.0825078	−	0.0317010i
$385$	1.98923e6	+	3.44545e6i	0.683963	+	1.18466i
$386$	2.31502e6			0.790837
$387$	1.15881e6	+	5.43527e6i	0.393311	+	1.84478i
$388$	1.28686e6			0.433962
$389$	1.96659e6	+	3.40623e6i	0.658930	+	1.14130i	0.980893	+	0.194548i	$0.0623240\pi$
$389$	1.96659e6	+	3.40623e6i	0.658930	+	1.14130i	−0.321963	+	0.946752i	$0.604343\pi$
$390$	−973991.	−	788224.i	−0.324260	−	0.262415i
$391$	−301257.	+	521792.i	−0.0996540	+	0.172606i
$392$	−785044.	+	1.35974e6i	−0.258035	+	0.446930i
$393$	−1.16420e6	−	942154.i	−0.380229	−	0.307709i
$394$	−468771.	−	811935.i	−0.152132	−	0.263500i
$395$	−2.10229e6			−0.677953
$396$	−1.73951e6	−	564014.i	−0.557429	−	0.180739i
$397$	1.48840e6			0.473960			0.236980	−	0.971514i	$-0.423842\pi$
$397$	1.48840e6			0.473960			0.236980	+	0.971514i	$0.423842\pi$
$398$	−401101.	−	694727.i	−0.126925	−	0.219840i
$399$	−5.85490e6	+	2.24956e6i	−1.84114	+	0.707402i
$400$	178458.	−	309098.i	0.0557680	−	0.0965930i
$401$	1.84020e6	−	3.18731e6i	0.571483	−	0.989837i	−0.424931	−	0.905226i	$-0.639702\pi$
$401$	1.84020e6	−	3.18731e6i	0.571483	−	0.989837i	0.996414	−	0.0846115i	$-0.0269649\pi$
$402$	−23918.8	+	151320.i	−0.00738200	+	0.0467015i
$403$	573091.	+	992622.i	0.175776	+	0.304454i
$404$	910407.			0.277512
$405$	−2.24299e6	+	1.00197e6i	−0.679500	+	0.303540i
$406$	943817.			0.284166
$407$	−1.92487e6	−	3.33398e6i	−0.575991	−	0.997646i
$408$	−196241.	+	1.24150e6i	−0.0583632	+	0.369229i
$409$	−290013.	+	502318.i	−0.0857254	+	0.148481i	−0.905700	−	0.423919i	$-0.860654\pi$
$409$	−290013.	+	502318.i	−0.0857254	+	0.148481i	0.819975	+	0.572400i	$0.193987\pi$
$410$	−1.45758e6	+	2.52460e6i	−0.428225	+	0.741707i
$411$	3.37849e6	−	1.29808e6i	0.986549	−	0.379050i
$412$	1.57608e6	+	2.72985e6i	0.457441	+	0.792311i
$413$	9.06073e6			2.61389
$414$	−442185.	−	143373.i	−0.126795	−	0.0411117i
$415$	−2.15619e6			−0.614563
$416$	−247302.	−	428339.i	−0.0700638	−	0.121354i
$417$	1.94569e6	+	1.57459e6i	0.547940	+	0.443433i
$418$	−1.86154e6	+	3.22427e6i	−0.521112	+	0.902592i
$419$	759450.	−	1.31541e6i	0.211331	−	0.366037i	−0.740800	−	0.671726i	$-0.765553\pi$
$419$	759450.	−	1.31541e6i	0.211331	−	0.366037i	0.952131	+	0.305689i	$0.0988868\pi$
$420$	1.63999e6	+	1.32720e6i	0.453647	+	0.367124i
$421$	−2.70128e6	−	4.67875e6i	−0.742787	−	1.28654i	−0.951222	−	0.308508i	$-0.900170\pi$
$421$	−2.70128e6	−	4.67875e6i	−0.742787	−	1.28654i	0.208435	−	0.978036i	$-0.433163\pi$
$422$	−2.15861e6			−0.590055
$423$	−880172.	−	4.12834e6i	−0.239175	−	1.12182i
$424$	−344997.			−0.0931967
$425$	878248.	+	1.52117e6i	0.235855	+	0.408513i
$426$	127142.	−	48850.3i	0.0339441	−	0.0130420i
$427$	423756.	−	733967.i	0.112472	−	0.194808i
$428$	187859.	−	325382.i	0.0495705	−	0.0858587i
$429$	−552908.	+	3.49792e6i	−0.145047	+	0.917627i
$430$	−1.90292e6	−	3.29596e6i	−0.496306	−	0.859628i
$431$	−3.04614e6			−0.789871			−0.394935	−	0.918709i	$-0.629233\pi$
$431$	−3.04614e6			−0.789871			−0.394935	+	0.918709i	$0.629233\pi$
$432$	−968350.	+	51649.3i	−0.249645	+	0.0133154i
$433$	−1.07293e6			−0.275011			−0.137505	−	0.990501i	$-0.543908\pi$
$433$	−1.07293e6			−0.275011			−0.137505	+	0.990501i	$0.543908\pi$
$434$	−964960.	−	1.67136e6i	−0.245915	−	0.425937i
$435$	117505.	−	743383.i	0.0297737	−	0.188360i
$436$	948397.	−	1.64267e6i	0.238932	−	0.413842i
$437$	−473203.	+	819612.i	−0.118534	+	0.205307i
$438$	176790.	−	67925.9i	0.0440323	−	0.0169180i
$439$	−3.81738e6	−	6.61190e6i	−0.945376	−	1.63744i	−0.754996	−	0.655729i	$-0.772361\pi$
$439$	−3.81738e6	−	6.61190e6i	−0.945376	−	1.63744i	−0.190380	−	0.981710i	$-0.560972\pi$
$440$	1.25231e6			0.308375
$441$	4.42774e6	−	3.99171e6i	1.08414	−	0.977378i
$442$	2.43411e6			0.592630
$443$	3.30067e6	+	5.71693e6i	0.799085	+	1.38406i	0.920213	+	0.391419i	$0.128016\pi$
$443$	3.30067e6	+	5.71693e6i	0.799085	+	1.38406i	−0.121127	+	0.992637i	$0.538651\pi$
$444$	−1.58693e6	−	1.28426e6i	−0.382033	−	0.309169i
$445$	419248.	−	726159.i	0.100362	−	0.173833i
$446$	−1.77034e6	+	3.06631e6i	−0.421424	+	0.729927i
$447$	3.38303e6	+	2.73779e6i	0.800824	+	0.648085i
$448$	416402.	+	721230.i	0.0980208	+	0.169777i
$449$	−5.52311e6			−1.29291			−0.646454	−	0.762953i	$-0.723749\pi$
$449$	−5.52311e6			−1.29291			−0.646454	+	0.762953i	$0.723749\pi$
$450$	−1.00652e6	+	907403.i	−0.234310	+	0.211236i
$451$	8.23922e6			1.90741
$452$	3574.42	+	6191.07i	0.000822923	+	0.00142534i
$453$	−415844.	+	159775.i	−0.0952104	+	0.0365816i
$454$	−636267.	+	1.10205e6i	−0.144877	+	0.250935i
$455$	2.04284e6	−	3.53830e6i	0.462600	−	0.801246i
$456$	−308248.	+	1.95010e6i	−0.0694206	+	0.439183i
$457$	−706717.	−	1.22407e6i	−0.158291	−	0.274167i	0.775962	−	0.630780i	$-0.217265\pi$
$457$	−706717.	−	1.22407e6i	−0.158291	−	0.274167i	−0.934252	+	0.356613i	$0.883932\pi$
$458$	1.97547e6			0.440056
$459$	2.16266e6	−	4.25420e6i	0.479132	−	0.942509i
$460$	318337.			0.0701444
$461$	−4.25416e6	−	7.36841e6i	−0.932312	−	1.61481i	−0.779359	−	0.626578i	$-0.784455\pi$
$461$	−4.25416e6	−	7.36841e6i	−0.932312	−	1.61481i	−0.152953	−	0.988234i	$-0.548878\pi$
$462$	930976.	−	5.88973e6i	0.202924	−	1.28378i
$463$	−2.04077e6	+	3.53472e6i	−0.442427	+	0.766307i	−0.997869	−	0.0652489i	$-0.979216\pi$
$463$	−2.04077e6	+	3.53472e6i	−0.442427	+	0.766307i	0.555442	+	0.831555i	$0.312549\pi$
$464$	148544.	−	257285.i	0.0320302	−	0.0554779i
$465$	−1.43656e6	+	551952.i	−0.308099	+	0.118377i
$466$	−2.32377e6	−	4.02489e6i	−0.495711	−	0.858597i
$467$	−5.38239e6			−1.14204			−0.571022	−	0.820935i	$-0.693453\pi$
$467$	−5.38239e6			−1.14204			−0.571022	+	0.820935i	$0.693453\pi$
$468$	391582.	+	1.83667e6i	0.0826435	+	0.387629i
$469$	−499545.			−0.104868
$470$	1.44536e6	+	2.50343e6i	0.301808	+	0.522746i
$471$	1.50565e6	+	1.21848e6i	0.312732	+	0.253085i
$472$	1.42603e6	−	2.46996e6i	0.294629	−	0.510312i
$473$	−5.37831e6	+	9.31550e6i	−1.10533	+	1.91449i
$474$	2.44931e6	+	1.98216e6i	0.500723	+	0.405221i
$475$	1.37952e6	+	2.38940e6i	0.280540	+	0.485909i
$476$	−4.09850e6			−0.829102
$477$	1.24605e6	+	404014.i	0.250749	+	0.0813019i
$478$	−4.63410e6			−0.927675
$479$	4.29153e6	+	7.43315e6i	0.854621	+	1.48025i	0.876997	+	0.480497i	$0.159544\pi$
$479$	4.29153e6	+	7.43315e6i	0.854621	+	1.48025i	−0.0223760	+	0.999750i	$0.507123\pi$
$480$	619907.	−	238180.i	0.122807	−	0.0471848i
$481$	−1.97675e6	+	3.42383e6i	−0.389573	+	0.674760i
$482$	1.64223e6	−	2.84442e6i	0.321970	−	0.557669i
$483$	236655.	−	1.49717e6i	0.0461580	−	0.292014i
$484$	−481319.	−	833668.i	−0.0933941	−	0.161763i
$485$	3.34607e6			0.645922
$486$	3.55794e6	+	947458.i	0.683295	+	0.181957i
$487$	−3.96670e6			−0.757891			−0.378946	−	0.925419i	$-0.623713\pi$
$487$	−3.96670e6			−0.757891			−0.378946	+	0.925419i	$0.623713\pi$
$488$	−133387.	−	231033.i	−0.0253550	−	0.0439161i
$489$	−398884.	+	2.52350e6i	−0.0754352	+	0.477234i
$490$	−2.04125e6	+	3.53556e6i	−0.384067	+	0.665224i
$491$	−2.88205e6	+	4.99185e6i	−0.539507	+	0.934454i	0.459424	+	0.888217i	$0.348056\pi$
$491$	−2.88205e6	+	4.99185e6i	−0.539507	+	0.934454i	−0.998931	+	0.0462362i	$0.985277\pi$
$492$	4.07851e6	−	1.56704e6i	0.759606	−	0.291855i
$493$	731033.	+	1.26619e6i	0.135463	+	0.234628i
$494$	3.82341e6			0.704909
$495$	−4.52305e6	−	1.46654e6i	−0.829695	−	0.269017i
$496$	−607486.			−0.110875
$497$	222064.	+	384627.i	0.0403262	+	0.0698471i
$498$	2.51210e6	+	2.03298e6i	0.453904	+	0.367332i
$499$	2.32003e6	−	4.01841e6i	0.417102	−	0.722442i	−0.578544	−	0.815651i	$-0.696379\pi$
$499$	2.32003e6	−	4.01841e6i	0.417102	−	0.722442i	0.995647	+	0.0932088i	$0.0297124\pi$
$500$	1.50409e6	−	2.60517e6i	0.269061	−	0.466026i
$501$	1.96703e6	+	1.59187e6i	0.350120	+	0.283343i
$502$	1.70471e6	+	2.95265e6i	0.301920	+	0.522941i
$503$	−2.73360e6			−0.481743			−0.240872	−	0.970557i	$-0.577433\pi$
$503$	−2.73360e6			−0.481743			−0.240872	+	0.970557i	$0.577433\pi$
$504$	−659340.	−	3.09255e6i	−0.115620	−	0.542301i
$505$	2.36722e6			0.413057
$506$	−449865.	−	779189.i	−0.0781099	−	0.135290i
$507$	−2.00799e6	+	771506.i	−0.346929	+	0.133297i
$508$	−1.55042e6	+	2.68541e6i	−0.266558	+	0.461692i
$509$	2.97841e6	−	5.15877e6i	0.509555	−	0.882574i	−0.490384	−	0.871506i	$-0.663144\pi$
$509$	2.97841e6	−	5.15877e6i	0.509555	−	0.882574i	0.999939	−	0.0110680i	$-0.00352313\pi$
$510$	−510262.	+	3.22812e6i	−0.0868696	+	0.549572i
$511$	308778.	+	534820.i	0.0523112	+	0.0906056i
$512$	262144.			0.0441942
$513$	3.39702e6	−	6.68234e6i	0.569908	−	1.12108i
$514$	5.20137e6			0.868380
$515$	4.09809e6	+	7.09810e6i	0.680869	+	1.17930i
$516$	−890584.	+	5.63419e6i	−0.147248	+	0.931553i
$517$	4.08507e6	−	7.07555e6i	0.672161	−	1.16422i
$518$	3.32841e6	−	5.76498e6i	0.545020	−	0.944003i
$519$	−5.59292e6	+	2.14890e6i	−0.911424	+	0.350186i
$520$	−643029.	−	1.11376e6i	−0.104285	−	0.180627i
$521$	−1.11813e7			−1.80468			−0.902339	−	0.431027i	$-0.858151\pi$
$521$	−1.11813e7			−1.80468			−0.902339	+	0.431027i	$0.858151\pi$
$522$	−837804.	+	755301.i	−0.134576	+	0.121323i
$523$	4.60970e6			0.736917			0.368458	−	0.929644i	$-0.379886\pi$
$523$	4.60970e6			0.736917			0.368458	+	0.929644i	$0.379886\pi$
$524$	−768604.	−	1.33126e6i	−0.122285	−	0.211804i
$525$	−3.43497e6	−	2.77982e6i	−0.543907	−	0.440169i
$526$	2.28915e6	−	3.96493e6i	0.360753	−	0.624843i
$527$	1.49482e6	−	2.58910e6i	0.234456	−	0.406090i
$528$	−1.45902e6	−	1.18075e6i	−0.227760	−	0.184320i
$529$	3.10382e6	+	5.37597e6i	0.482233	+	0.835252i
$530$	−897054.			−0.138717
$531$	−8.04299e6	+	7.25095e6i	−1.23789	+	1.11599i
$532$	−6.43779e6			−0.986183
$533$	−4.23063e6	−	7.32767e6i	−0.645041	−	1.11724i
$534$	−1.17312e6	+	450733.i	−0.178028	+	0.0684016i
$535$	488468.	−	846052.i	0.0737823	−	0.127795i
$536$	−78621.6	+	136177.i	−0.0118203	+	0.0204734i
$537$	1.24609e6	−	7.88327e6i	0.186472	−	1.17970i
$538$	−3.08190e6	−	5.33801e6i	−0.459053	−	0.795103i
$539$	1.15386e7			1.71072
$540$	−2.51789e6	+	134298.i	−0.371579	+	0.0198191i
$541$	−8.65572e6			−1.27148			−0.635741	−	0.771902i	$-0.719305\pi$
$541$	−8.65572e6			−1.27148			−0.635741	+	0.771902i	$0.719305\pi$
$542$	−2.84794e6	−	4.93277e6i	−0.416421	−	0.721262i
$543$	695662.	−	4.40104e6i	0.101251	−	0.640554i
$544$	−645048.	+	1.11726e6i	−0.0934534	+	0.161866i
$545$	2.46600e6	−	4.27124e6i	0.355633	−	0.615975i
$546$	−5.71615e6	+	2.19625e6i	−0.820582	+	0.315283i
$547$	−581626.	−	1.00741e6i	−0.0831143	−	0.143958i	0.821472	−	0.570249i	$-0.193153\pi$
$547$	−581626.	−	1.00741e6i	−0.0831143	−	0.143958i	−0.904586	+	0.426291i	$0.859820\pi$
$548$	3.71484e6			0.528431
$549$	211207.	+	990641.i	0.0299073	+	0.140277i
$550$	−2.62297e6			−0.369731
$551$	1.14828e6	+	1.98888e6i	0.161127	+	0.279081i
$552$	−370884.	−	300147.i	−0.0518073	−	0.0419262i
$553$	−5.13715e6	+	8.89781e6i	−0.714347	+	1.23729i
$554$	−3.19204e6	+	5.52877e6i	−0.441869	+	0.765339i
$555$	−4.12631e6	−	3.33931e6i	−0.568629	−	0.460176i
$556$	1.28454e6	+	2.22489e6i	0.176223	+	0.305227i
$557$	1.23037e7			1.68034			0.840168	−	0.542326i	$-0.182456\pi$
$557$	1.23037e7			1.68034			0.840168	+	0.542326i	$0.182456\pi$
$558$	2.19410e6	+	711407.i	0.298312	+	0.0967236i
$559$	1.10465e7			1.49519
$560$	1.08272e6	+	1.87533e6i	0.145897	+	0.252701i
$561$	8.62251e6	−	3.31293e6i	1.15672	−	0.444432i
$562$	−803067.	+	1.39095e6i	−0.107253	+	0.185768i
$563$	2.76949e6	−	4.79690e6i	0.368239	−	0.637808i	−0.621052	−	0.783770i	$-0.713294\pi$
$563$	2.76949e6	−	4.79690e6i	0.368239	−	0.637808i	0.989290	+	0.145962i	$0.0466276\pi$
$564$	676439.	−	4.27943e6i	0.0895429	−	0.566484i
$565$	9294.13	+	16097.9i	0.00122486	+	0.00212152i
$566$	4.28466e6			0.562180
$567$	−1.24020e6	+	1.19417e7i	−0.162007	+	1.55994i
$568$	139799.			0.0181817
$569$	−6.91495e6	−	1.19770e7i	−0.895382	−	1.55085i	−0.833331	−	0.552775i	$-0.813569\pi$
$569$	−6.91495e6	−	1.19770e7i	−0.895382	−	1.55085i	−0.0620514	−	0.998073i	$-0.519764\pi$
$570$	−801501.	+	5.07062e6i	−0.103328	+	0.653693i
$571$	−990947.	+	1.71637e6i	−0.127192	+	0.220303i	−0.922588	−	0.385787i	$-0.873930\pi$
$571$	−990947.	+	1.71637e6i	−0.127192	+	0.220303i	0.795396	+	0.606091i	$0.207263\pi$
$572$	−1.81742e6	+	3.14786e6i	−0.232255	+	0.402278i
$573$	542071.	−	208274.i	0.0689715	−	0.0265001i
$574$	7.12346e6	+	1.23382e7i	0.902425	+	1.56305i
$575$	−666760.			−0.0841007
$576$	−946803.	−	306988.i	−0.118906	−	0.0385536i
$577$	9.36673e6			1.17125			0.585623	−	0.810583i	$-0.300850\pi$
$577$	9.36673e6			1.17125			0.585623	+	0.810583i	$0.300850\pi$
$578$	−334780.	−	579855.i	−0.0416811	−	0.0721938i
$579$	−7.01309e6	−	5.67550e6i	−0.869387	−	0.703571i
$580$	386241.	−	668989.i	0.0476747	−	0.0825750i
$581$	−5.26886e6	+	9.12593e6i	−0.647554	+	1.12160i
$582$	−3.89839e6	−	3.15486e6i	−0.477066	−	0.386076i
$583$	1.26769e6	+	2.19570e6i	0.154469	+	0.267549i
$584$	194390.			0.0235853
$585$	1.01818e6	+	4.77567e6i	0.123009	+	0.576958i
$586$	−2.87064e6			−0.345330
$587$	929269.	+	1.60954e6i	0.111313	+	0.192800i	0.916300	−	0.400493i	$-0.131161\pi$
$587$	929269.	+	1.60954e6i	0.111313	+	0.192800i	−0.804987	+	0.593293i	$0.797828\pi$
$588$	5.71172e6	−	2.19455e6i	0.681277	−	0.261759i
$589$	2.34801e6	−	4.06687e6i	0.278876	−	0.483028i
$590$	3.70795e6	−	6.42235e6i	0.438534	−	0.759563i
$591$	−570451.	+	3.60890e6i	−0.0671815	+	0.425017i
$592$	−1.04769e6	−	1.81466e6i	−0.122865	−	0.212809i
$593$	1.50844e6			0.176154			0.0880770	−	0.996114i	$-0.471928\pi$
$593$	1.50844e6			0.176154			0.0880770	+	0.996114i	$0.471928\pi$
$594$	3.88692e6	+	5.97320e6i	0.452001	+	0.694610i
$595$	−1.06568e7			−1.23406
$596$	2.23348e6	+	3.86850e6i	0.257553	+	0.446094i
$597$	−488103.	+	3.08793e6i	−0.0560500	+	0.354595i
$598$	−461989.	+	800188.i	−0.0528297	+	0.0915038i
$599$	−6.50791e6	+	1.12720e7i	−0.741096	+	1.28362i	0.210901	+	0.977507i	$0.432360\pi$
$599$	−6.50791e6	+	1.12720e7i	−0.741096	+	1.28362i	−0.951997	+	0.306108i	$0.900973\pi$
$600$	−1.29840e6	+	498869.i	−0.147242	+	0.0565729i
$601$	6.92629e6	+	1.19967e7i	0.782194	+	1.35480i	0.930661	+	0.365882i	$0.119233\pi$
$601$	6.92629e6	+	1.19967e7i	0.782194	+	1.35480i	−0.148467	+	0.988917i	$0.547434\pi$
$602$	−1.85999e7			−2.09180
$603$	443435.	−	399767.i	0.0496634	−	0.0447727i
$604$	−457243.			−0.0509981
$605$	−1.25152e6	−	2.16769e6i	−0.139011	−	0.240773i
$606$	−2.75797e6	−	2.23195e6i	−0.305076	−	0.246890i
$607$	4.75435e6	−	8.23478e6i	0.523745	−	0.907153i	−0.475873	−	0.879514i	$-0.657868\pi$
$607$	4.75435e6	−	8.23478e6i	0.523745	−	0.907153i	0.999618	−	0.0276388i	$-0.00879883\pi$
$608$	−1.01322e6	+	1.75495e6i	−0.111159	+	0.192533i
$609$	−2.85919e6	−	2.31386e6i	−0.312391	−	0.252810i
$610$	−346830.	−	600726.i	−0.0377391	−	0.0653660i
$611$	−8.39032e6			−0.909234
$612$	3.63815e6	−	3.27987e6i	0.392646	−	0.353980i
$613$	−1.65462e7			−1.77848			−0.889238	−	0.457445i	$-0.848765\pi$
$613$	−1.65462e7			−1.77848			−0.889238	+	0.457445i	$0.848765\pi$
$614$	4.51242e6	+	7.81574e6i	0.483046	+	0.836661i
$615$	1.06049e7	−	4.07458e6i	1.13062	−	0.434405i
$616$	3.06014e6	−	5.30032e6i	0.324930	−	0.562795i
$617$	2.75765e6	−	4.77638e6i	0.291626	−	0.505111i	−0.682569	−	0.730822i	$-0.739137\pi$
$617$	2.75765e6	−	4.77638e6i	0.291626	−	0.505111i	0.974194	+	0.225711i	$0.0724705\pi$
$618$	1.91794e6	−	1.21337e7i	0.202006	−	1.27797i
$619$	−1.24124e6	−	2.14989e6i	−0.130205	−	0.225522i	0.793550	−	0.608505i	$-0.208230\pi$
$619$	−1.24124e6	−	2.14989e6i	−0.130205	−	0.225522i	−0.923756	+	0.382982i	$0.874897\pi$
$620$	−1.57957e6			−0.165029
$621$	988056.	+	1.51839e6i	0.102814	+	0.157999i
$622$	7.17752e6			0.743872
$623$	−2.04895e6	−	3.54888e6i	−0.211500	−	0.366329i
$624$	−300943.	+	1.90389e6i	−0.0309402	+	0.195740i
$625$	1.73248e6	−	3.00074e6i	0.177406	−	0.307276i
$626$	1.12758e6	−	1.95303e6i	0.115004	−	0.199192i
$627$	1.35439e7	−	5.20383e6i	1.37587	−	0.528633i
$628$	994032.	+	1.72171e6i	0.100578	+	0.174205i
$629$	1.03121e7			1.03925
$630$	−1.71440e6	−	8.04119e6i	−0.172092	−	0.807177i
$631$	−9.16852e6			−0.916697			−0.458349	−	0.888772i	$-0.651559\pi$
$631$	−9.16852e6			−0.916697			−0.458349	+	0.888772i	$0.651559\pi$
$632$	1.61703e6	+	2.80078e6i	0.161037	+	0.278925i
$633$	6.53925e6	+	5.29204e6i	0.648662	+	0.524945i
$634$	6.36613e6	−	1.10265e7i	0.629003	−	1.08946i
$635$	−4.03138e6	+	6.98256e6i	−0.396753	+	0.687196i
$636$	1.04513e6	+	845794.i	0.102453	+	0.0829128i
$637$	−5.92476e6	−	1.02620e7i	−0.578525	−	1.00204i
$638$	−2.18330e6			−0.212354
$639$	−504923.	−	163715.i	−0.0489185	−	0.0158612i
$640$	681622.			0.0657799
$641$	994072.	+	1.72178e6i	0.0955593	+	0.165514i	0.909842	−	0.414955i	$-0.136203\pi$
$641$	994072.	+	1.72178e6i	0.0955593	+	0.165514i	−0.814283	+	0.580469i	$0.802869\pi$
$642$	−1.36680e6	+	525152.i	−0.130879	+	0.0502860i
$643$	2.62237e6	−	4.54208e6i	0.250130	−	0.433239i	−0.713431	−	0.700725i	$-0.752860\pi$
$643$	2.62237e6	−	4.54208e6i	0.250130	−	0.433239i	0.963562	+	0.267487i	$0.0861932\pi$
$644$	777889.	−	1.34734e6i	0.0739099	−	0.128016i
$645$	−2.31568e6	+	1.46499e7i	−0.219169	+	1.38655i
$646$	−4.98638e6	−	8.63667e6i	−0.470115	−	0.814263i
$647$	9.94212e6			0.933723			0.466862	−	0.884330i	$-0.345385\pi$
$647$	9.94212e6			0.933723			0.466862	+	0.884330i	$0.345385\pi$
$648$	3.06013e6	+	2.21754e6i	0.286287	+	0.207460i
$649$	−2.09598e7			−1.95333
$650$	1.34683e6	+	2.33278e6i	0.125034	+	0.216566i
$651$	−1.17427e6	+	7.42889e6i	−0.108596	+	0.687023i
$652$	−1.31114e6	+	2.27096e6i	−0.120790	+	0.209214i
$653$	1.21132e6	−	2.09806e6i	0.111167	−	0.192547i	−0.805074	−	0.593174i	$-0.797875\pi$
$653$	1.21132e6	−	2.09806e6i	0.111167	−	0.192547i	0.916241	+	0.400628i	$0.131208\pi$
$654$	−6.90023e6	+	2.65120e6i	−0.630840	+	0.242380i
$655$	−1.99851e6	−	3.46152e6i	−0.182013	−	0.315256i
$656$	4.48454e6			0.406872
$657$	−702091.	−	227643.i	−0.0634570	−	0.0205751i
$658$	1.41275e7			1.27204
$659$	−7.70304e6	−	1.33421e7i	−0.690953	−	1.19677i	−0.971526	−	0.236933i	$-0.923858\pi$
$659$	−7.70304e6	−	1.33421e7i	−0.690953	−	1.19677i	0.280573	−	0.959833i	$-0.409476\pi$
$660$	−3.79373e6	−	3.07016e6i	−0.339005	−	0.274347i
$661$	−3.40975e6	+	5.90586e6i	−0.303542	+	0.525751i	−0.976936	−	0.213534i	$-0.931503\pi$
$661$	−3.40975e6	+	5.90586e6i	−0.303542	+	0.525751i	0.673393	+	0.739284i	$0.264836\pi$
$662$	15049.9	−	26067.2i	0.00133471	−	0.00231179i
$663$	−7.37384e6	−	5.96745e6i	−0.651493	−	0.527236i
$664$	1.65849e6	+	2.87259e6i	0.145980	+	0.252845i
$665$	−1.67394e7			−1.46786
$666$	1.65894e6	+	7.78104e6i	0.144925	+	0.679754i
$667$	−554995.			−0.0483030
$668$	1.29864e6	+	2.24930e6i	0.112602	+	0.195032i
$669$	1.28804e7	−	4.94889e6i	1.11266	−	0.427506i
$670$	−204430.	+	354084.i	−0.0175937	+	0.0304733i
$671$	−980259.	+	1.69786e6i	−0.0840494	+	0.145578i
$672$	506723.	−	3.20573e6i	0.0432860	−	0.273845i
$673$	114441.	+	198218.i	0.00973969	+	0.0168696i	0.870854	−	0.491541i	$-0.163566\pi$
$673$	114441.	+	198218.i	0.00973969	+	0.0168696i	−0.861114	+	0.508411i	$0.830233\pi$
$674$	−5.87865e6			−0.498457
$675$	5.27373e6	−	281287.i	0.445511	−	0.0237624i
$676$	−2.20789e6			−0.185828
$677$	1.00487e7	+	1.74048e7i	0.842629	+	1.45948i	0.887665	+	0.460491i	$0.152327\pi$
$677$	1.00487e7	+	1.74048e7i	0.842629	+	1.45948i	−0.0450356	+	0.998985i	$0.514340\pi$
$678$	4349.73	−	27518.2i	0.000363403	−	0.00229903i
$679$	8.17644e6	−	1.41620e7i	0.680597	−	1.17883i
$680$	−1.67724e6	+	2.90507e6i	−0.139099	+	0.240926i
$681$	4.62928e6	−	1.77865e6i	0.382512	−	0.146968i
$682$	2.23221e6	+	3.86629e6i	0.183769	+	0.318298i
$683$	1.34916e7			1.10665			0.553325	−	0.832965i	$-0.313359\pi$
$683$	1.34916e7			1.10665			0.553325	+	0.832965i	$0.313359\pi$
$684$	5.71467e6	−	5.15191e6i	0.467037	−	0.421045i
$685$	9.65924e6			0.786533
$686$	3.14156e6	+	5.44135e6i	0.254880	+	0.441465i
$687$	−5.98447e6	−	4.84307e6i	−0.483764	−	0.391497i
$688$	−2.92737e6	+	5.07035e6i	−0.235780	+	0.408382i
$689$	1.30185e6	−	2.25488e6i	0.104475	−	0.180957i
$690$	−964366.	−	780435.i	−0.0771115	−	0.0624042i
$691$	−2.16664e6	−	3.75273e6i	−0.172620	−	0.298987i	0.766715	−	0.641988i	$-0.221890\pi$
$691$	−2.16664e6	−	3.75273e6i	−0.172620	−	0.298987i	−0.939335	+	0.343001i	$0.888557\pi$
$692$	−6.14972e6			−0.488191
$693$	−1.72595e7	+	1.55599e7i	−1.36520	+	1.23076i
$694$	−1.04919e7			−0.826903
$695$	3.34005e6	+	5.78513e6i	0.262295	+	0.454309i
$696$	−1.08076e6	+	415247.i	−0.0845678	+	0.0324925i
$697$	−1.10349e7	+	1.91131e7i	−0.860376	+	1.49021i
$698$	−2.32931e6	+	4.03448e6i	−0.180962	+	0.313436i
$699$	−2.82781e6	+	1.78899e7i	−0.218906	+	1.38489i
$700$	−2.26777e6	−	3.92789e6i	−0.174926	−	0.302980i
$701$	−4.00999e6			−0.308211			−0.154106	−	0.988054i	$-0.549250\pi$
$701$	−4.00999e6			−0.308211			−0.154106	+	0.988054i	$0.549250\pi$
$702$	3.31652e6	−	6.52398e6i	0.254003	−	0.499654i
$703$	1.61978e7			1.23614
$704$	−963248.	−	1.66839e6i	−0.0732498	−	0.126872i
$705$	1.75886e6	−	1.11273e7i	0.133278	−	0.843172i
$706$	−6.29354e6	+	1.09007e7i	−0.475208	+	0.823084i
$707$	5.78454e6	−	1.00191e7i	0.435231	−	0.753843i
$708$	−1.03754e7	+	3.98641e6i	−0.777893	+	0.298881i
$709$	−2.57127e6	−	4.45358e6i	−0.192102	−	0.332731i	0.753844	−	0.657053i	$-0.228197\pi$
$709$	−2.57127e6	−	4.45358e6i	−0.192102	−	0.332731i	−0.945947	+	0.324322i	$0.894864\pi$
$710$	363504.			0.0270622
$711$	−2.56044e6	−	1.20094e7i	−0.189951	−	0.890940i
$712$	−1.28990e6			−0.0953581
$713$	567428.	+	982813.i	0.0418010	+	0.0724014i
$714$	1.24159e7	+	1.00479e7i	0.911453	+	0.737614i
$715$	−4.72562e6	+	8.18501e6i	−0.345695	+	0.598762i
$716$	4.09593e6	−	7.09435e6i	0.298586	−	0.517166i
$717$	1.40385e7	+	1.13610e7i	1.01982	+	0.825310i
$718$	1.44169e6	+	2.49709e6i	0.104367	+	0.180769i
$719$	−1.15318e6			−0.0831906			−0.0415953	−	0.999135i	$-0.513244\pi$
$719$	−1.15318e6			−0.0831906			−0.0415953	+	0.999135i	$0.513244\pi$
$720$	−2.46186e6	−	798225.i	−0.176983	−	0.0573844i
$721$	4.00564e7			2.86968
$722$	−2.88023e6	−	4.98871e6i	−0.205629	−	0.356160i
$723$	−1.19483e7	+	4.59077e6i	−0.850083	+	0.326618i
$724$	2.28666e6	−	3.96061e6i	0.162127	−	0.280812i
$725$	−808984.	+	1.40120e6i	−0.0571603	+	0.0990046i
$726$	−585720.	+	3.70550e6i	−0.0412428	+	0.260919i
$727$	9.27449e6	+	1.60639e7i	0.650810	+	1.12724i	0.982927	+	0.183997i	$0.0589038\pi$
$727$	9.27449e6	+	1.60639e7i	0.650810	+	1.12724i	−0.332117	+	0.943238i	$0.607763\pi$
$728$	−6.28522e6			−0.439533
$729$	−8.45558e6	−	1.15929e7i	−0.589284	−	0.807926i
$730$	505449.			0.0351051
$731$	−1.44065e7	−	2.49529e7i	−0.997163	−	1.72714i
$732$	−162319.	+	1.02690e6i	−0.0111968	+	0.0708352i
$733$	2.05765e6	−	3.56395e6i	0.141453	−	0.245003i	−0.786591	−	0.617474i	$-0.788156\pi$
$733$	2.05765e6	−	3.56395e6i	0.141453	−	0.245003i	0.928044	+	0.372471i	$0.121489\pi$
$734$	−165033.	+	285845.i	−0.0113066	+	0.0195835i
$735$	1.48515e7	−	5.70623e6i	1.01403	−	0.389610i
$736$	−244858.	−	424106.i	−0.0166617	−	0.0288589i
$737$	1.15558e6			0.0783666
$738$	−1.61971e7	−	5.25170e6i	−1.09470	−	0.354943i
$739$	−2.27852e7			−1.53477			−0.767384	−	0.641188i	$-0.778442\pi$
$739$	−2.27852e7			−1.53477			−0.767384	+	0.641188i	$0.778442\pi$
$740$	−2.72419e6	−	4.71844e6i	−0.182877	−	0.316752i
$741$	−1.15826e7	−	9.37345e6i	−0.774924	−	0.627125i
$742$	−2.19204e6	+	3.79672e6i	−0.146163	+	0.253162i
$743$	1.05194e7	−	1.82202e7i	0.699068	−	1.21082i	−0.269721	−	0.962938i	$-0.586932\pi$
$743$	1.05194e7	−	1.82202e7i	0.699068	−	1.21082i	0.968790	−	0.247884i	$-0.0797351\pi$
$744$	1.84031e6	+	1.48931e6i	0.121887	+	0.0986400i
$745$	5.80745e6	+	1.00588e7i	0.383349	+	0.663980i
$746$	2.12121e7			1.39552
$747$	−2.62609e6	−	1.23173e7i	−0.172190	−	0.807635i
$748$	9.48092e6			0.619578
$749$	−2.38724e6	−	4.13482e6i	−0.155486	−	0.269310i
$750$	−1.09433e7	+	4.20462e6i	−0.710387	+	0.272944i
$751$	−1.03484e7	+	1.79240e7i	−0.669537	+	1.15967i	0.308497	+	0.951225i	$0.400174\pi$
$751$	−1.03484e7	+	1.79240e7i	−0.669537	+	1.15967i	−0.978034	+	0.208446i	$0.933159\pi$
$752$	2.22347e6	−	3.85116e6i	0.143379	−	0.248340i
$753$	2.07448e6	−	1.31240e7i	0.133328	−	0.843487i
$754$	1.12107e6	+	1.94175e6i	0.0718131	+	0.124384i
$755$	−1.18891e6			−0.0759072
$756$	−5.58429e6	+	1.09850e7i	−0.355356	+	0.699027i
$757$	1.22154e7			0.774761			0.387380	−	0.921920i	$-0.373380\pi$
$757$	1.22154e7			0.774761			0.387380	+	0.921920i	$0.373380\pi$
$758$	99069.5	+	171593.i	0.00626278	+	0.0108475i
$759$	−547444.	+	3.46335e6i	−0.0344933	+	0.218219i
$760$	−2.63455e6	+	4.56318e6i	−0.165452	+	0.286572i
$761$	−642893.	+	1.11352e6i	−0.0402417	+	0.0697007i	−0.885445	−	0.464745i	$-0.846146\pi$
$761$	−642893.	+	1.11352e6i	−0.0402417	+	0.0697007i	0.845203	+	0.534445i	$0.179479\pi$
$762$	1.12804e7	−	4.33414e6i	0.703780	−	0.270405i
$763$	−1.20518e7	−	2.08744e7i	−0.749449	−	1.29808i
$764$	596037.			0.0369436
$765$	9.45984e6	−	8.52827e6i	0.584427	−	0.526874i
$766$	−1.53743e7			−0.946723
$767$	1.07623e7	+	1.86409e7i	0.660570	+	1.14414i
$768$	−794135.	−	642672.i	−0.0485838	−	0.0393175i
$769$	5.43009e6	−	9.40520e6i	0.331125	−	0.573525i	−0.651608	−	0.758556i	$-0.725905\pi$
$769$	5.43009e6	−	9.40520e6i	0.331125	−	0.573525i	0.982733	+	0.185031i	$0.0592386\pi$
$770$	7.95692e6	−	1.37818e7i	0.483635	−	0.837681i
$771$	−1.57569e7	−	1.27517e7i	−0.954632	−	0.772557i
$772$	−4.63004e6	−	8.01947e6i	−0.279603	−	0.484287i
$773$	−7.80047e6			−0.469540			−0.234770	−	0.972051i	$-0.575434\pi$
$773$	−7.80047e6			−0.469540			−0.234770	+	0.972051i	$0.575434\pi$
$774$	1.65107e7	−	1.48848e7i	0.990634	−	0.893080i
$775$	3.30842e6			0.197864
$776$	−2.57372e6	−	4.45781e6i	−0.153429	−	0.265746i
$777$	−2.42164e7	+	9.30441e6i	−1.43899	+	0.552887i
$778$	7.86635e6	−	1.36249e7i	0.465934	−	0.807021i
$779$	−1.73333e7	+	3.00222e7i	−1.02338	+	1.77255i
$780$	−782507.	+	4.95045e6i	−0.0460523	+	0.291346i
$781$	−513693.	−	889742.i	−0.0301353	−	0.0521959i
$782$	2.41005e6			0.140932
$783$	4.38972e6	−	234137.i	0.255878	−	0.0136479i
$784$	6.28035e6			0.364917
$785$	2.58466e6	+	4.47676e6i	0.149703	+	0.259293i
$786$	−935320.	+	5.91721e6i	−0.0540012	+	0.341634i
$787$	−2.36760e6	+	4.10081e6i	−0.136261	+	0.236011i	−0.926079	−	0.377331i	$-0.876842\pi$
$787$	−2.36760e6	+	4.10081e6i	−0.136261	+	0.236011i	0.789817	+	0.613342i	$0.210175\pi$
$788$	−1.87508e6	+	3.24774e6i	−0.107573	+	0.186323i
$789$	−1.66551e7	+	6.39921e6i	−0.952479	+	0.365960i
$790$	4.20458e6	+	7.28255e6i	0.239693	+	0.415160i
$791$	90844.4			0.00516246
$792$	1.52523e6	+	7.15388e6i	0.0864015	+	0.405255i
$793$	2.01335e6			0.113694
$794$	−2.97679e6	−	5.15595e6i	−0.167570	−	0.290240i
$795$	2.71752e6	+	2.19922e6i	0.152495	+	0.123410i
$796$	−1.60440e6	+	2.77891e6i	−0.0897493	+	0.155450i
$797$	2.59183e6	−	4.48918e6i	0.144531	−	0.250335i	−0.784667	−	0.619918i	$-0.787166\pi$
$797$	2.59183e6	−	4.48918e6i	0.144531	−	0.250335i	0.929198	+	0.369583i	$0.120499\pi$
$798$	1.95025e7	+	1.57829e7i	1.08414	+	0.877361i
$799$	1.09424e7	+	1.89528e7i	0.606383	+	1.05029i
$800$	−1.42766e6			−0.0788679
$801$	4.65883e6	+	1.51056e6i	0.256564	+	0.0831874i
$802$	−1.47216e7			−0.808199
$803$	−714285.	−	1.23718e6i	−0.0390915	−	0.0677085i
$804$	572025.	−	219783.i	0.0312087	−	0.0119909i
$805$	2.02265e6	−	3.50333e6i	0.110010	−	0.190542i
$806$	2.29236e6	−	3.97049e6i	0.124293	−	0.215281i
$807$	−3.75039e6	+	2.37265e7i	−0.202718	+	1.28248i
$808$	−1.82081e6	−	3.15374e6i	−0.0981154	−	0.169941i
$809$	7.85790e6			0.422119			0.211060	−	0.977473i	$-0.432309\pi$
$809$	7.85790e6			0.422119			0.211060	+	0.977473i	$0.432309\pi$
$810$	7.95689e6	+	5.76600e6i	0.426119	+	0.308789i
$811$	2.34495e7			1.25193			0.625967	−	0.779849i	$-0.284704\pi$
$811$	2.34495e7			1.25193			0.625967	+	0.779849i	$0.284704\pi$
$812$	−1.88763e6	−	3.26948e6i	−0.100468	−	0.174016i
$813$	−3.46567e6	+	2.19253e7i	−0.183891	+	1.16337i
$814$	−7.69949e6	+	1.33359e7i	−0.407287	+	0.705443i
$815$	−3.40920e6	+	5.90491e6i	−0.179787	+	0.311400i
$816$	4.69316e6	−	1.80320e6i	0.246740	−	0.0948022i
$817$	−2.26293e7	−	3.91951e7i	−1.18608	−	2.05436i
$818$	2.32011e6			0.121234
$819$	2.27007e7	+	7.36041e6i	1.18258	+	0.383435i
$820$	1.16606e7			0.605601
$821$	1.29037e7	+	2.23499e7i	0.668125	+	1.15723i	0.978428	+	0.206589i	$0.0662362\pi$
$821$	1.29037e7	+	2.23499e7i	0.668125	+	1.15723i	−0.310303	+	0.950638i	$0.600430\pi$
$822$	−1.12537e7	−	9.10728e6i	−0.580918	−	0.470121i
$823$	−5.93578e6	+	1.02811e7i	−0.305477	+	0.529101i	−0.977367	−	0.211549i	$-0.932149\pi$
$823$	−5.93578e6	+	1.02811e7i	−0.305477	+	0.529101i	0.671891	+	0.740650i	$0.265482\pi$
$824$	6.30432e6	−	1.09194e7i	0.323460	−	0.560249i
$825$	7.94598e6	+	6.43046e6i	0.406455	+	0.328933i
$826$	−1.81215e7	−	3.13873e7i	−0.924151	−	1.60068i
$827$	−4.70487e6			−0.239213			−0.119606	−	0.992821i	$-0.538163\pi$
$827$	−4.70487e6			−0.239213			−0.119606	+	0.992821i	$0.538163\pi$
$828$	387713.	+	1.81852e6i	0.0196533	+	0.0921811i
$829$	−1.00951e7			−0.510183			−0.255091	−	0.966917i	$-0.582106\pi$
$829$	−1.00951e7			−0.510183			−0.255091	+	0.966917i	$0.582106\pi$
$830$	4.31238e6	+	7.46925e6i	0.217281	+	0.376341i
$831$	2.32242e7	−	8.92318e6i	1.16664	−	0.448247i
$832$	−989207.	+	1.71336e6i	−0.0495426	+	0.0858103i
$833$	−1.54538e7	+	2.67668e7i	−0.771656	+	1.33655i
$834$	1.56317e6	−	9.88925e6i	0.0778200	−	0.492321i
$835$	3.37669e6	+	5.84859e6i	0.167600	+	0.290292i
$836$	1.48923e7			0.736963
$837$	−4.90268e6	−	7.53417e6i	−0.241891	−	0.371725i
$838$	−6.07560e6			−0.298868
$839$	−3.68716e6	−	6.38634e6i	−0.180837	−	0.313218i	0.761329	−	0.648366i	$-0.224547\pi$
$839$	−3.68716e6	−	6.38634e6i	−0.180837	−	0.313218i	−0.942166	+	0.335147i	$0.891214\pi$
$840$	1.31757e6	−	8.33549e6i	0.0644282	−	0.407599i
$841$	9.58220e6	−	1.65968e7i	0.467170	−	0.809162i
$842$	−1.08051e7	+	1.87150e7i	−0.525229	+	0.909724i
$843$	5.84286e6	−	2.24493e6i	0.283176	−	0.108801i
$844$	4.31721e6	+	7.47763e6i	0.208616	+	0.361333i
$845$	−5.74092e6			−0.276592
$846$	−1.25406e7	+	1.13057e7i	−0.602412	+	0.543089i
$847$	−1.22328e7			−0.585892
$848$	689994.	+	1.19510e6i	0.0329500	+	0.0570711i
$849$	−1.29799e7	−	1.05043e7i	−0.618019	−	0.500145i
$850$	3.51299e6	−	6.08468e6i	0.166775	−	0.288862i
$851$	−1.95721e6	+	3.38999e6i	−0.0926434	+	0.160463i
$852$	−423506.	−	342732.i	−0.0199876	−	0.0161754i
$853$	−1.15979e7	−	2.00882e7i	−0.545769	−	0.945299i	−0.998558	−	0.0536815i	$-0.982904\pi$
$853$	−1.15979e7	−	2.00882e7i	−0.545769	−	0.945299i	0.452790	−	0.891617i	$-0.350429\pi$
$854$	−3.39005e6			−0.159060
$855$	1.48592e7	−	1.33959e7i	0.695151	−	0.626695i
$856$	−1.50288e6			−0.0701033
$857$	−4.71610e6	−	8.16852e6i	−0.219346	−	0.379919i	0.735262	−	0.677783i	$-0.237059\pi$
$857$	−4.71610e6	−	8.16852e6i	−0.219346	−	0.379919i	−0.954608	+	0.297864i	$0.903726\pi$
$858$	1.32230e7	−	5.08051e6i	0.613212	−	0.235607i
$859$	−7.97110e6	+	1.38064e7i	−0.368583	+	0.638405i	−0.989344	−	0.145595i	$-0.953490\pi$
$859$	−7.97110e6	+	1.38064e7i	−0.368583	+	0.638405i	0.620761	+	0.784000i	$0.286824\pi$
$860$	−7.61169e6	+	1.31838e7i	−0.350942	+	0.607849i
$861$	8.66859e6	−	5.48410e7i	0.398511	−	2.52114i
$862$	6.09227e6	+	1.05521e7i	0.279261	+	0.483695i
$863$	−2.89248e7			−1.32203			−0.661017	−	0.750371i	$-0.729875\pi$
$863$	−2.89248e7			−1.32203			−0.661017	+	0.750371i	$0.729875\pi$
$864$	2.11562e6	+	3.25117e6i	0.0964169	+	0.148168i
$865$	−1.59904e7			−0.726639
$866$	2.14585e6	+	3.71672e6i	0.0972310	+	0.168409i
$867$	−407396.	+	2.57735e6i	−0.0184064	+	0.116446i
$868$	−3.85984e6	+	6.68544e6i	−0.173888	+	0.301183i
$869$	1.18836e7	−	2.05830e7i	0.533824	−	0.924610i
$870$	−2.81016e6	+	1.07972e6i	−0.125873	+	0.0483628i
$871$	−593361.	−	1.02773e6i	−0.0265017	−	0.0459023i
$872$	−7.58717e6			−0.337900
$873$	4.07528e6	+	1.91146e7i	0.180976	+	0.848846i
$874$	3.78562e6			0.167633
$875$	−1.91134e7	−	3.31054e7i	−0.843953	−	1.46177i
$876$	−588881.	−	476566.i	−0.0259279	−	0.0209827i
$877$	8.40397e6	−	1.45561e7i	0.368965	−	0.639066i	−0.620439	−	0.784255i	$-0.713046\pi$
$877$	8.40397e6	−	1.45561e7i	0.368965	−	0.639066i	0.989404	+	0.145188i	$0.0463788\pi$
$878$	−1.52695e7	+	2.64476e7i	−0.668482	+	1.15784i
$879$	8.69627e6	+	7.03765e6i	0.379630	+	0.307224i
$880$	−2.50462e6	−	4.33813e6i	−0.109027	−	0.188841i
$881$	2.56183e7			1.11202			0.556008	−	0.831177i	$-0.312332\pi$
$881$	2.56183e7			1.11202			0.556008	+	0.831177i	$0.312332\pi$
$882$	−2.26832e7	−	7.35471e6i	−0.981820	−	0.318342i
$883$	1.53830e7			0.663955			0.331978	−	0.943287i	$-0.392284\pi$
$883$	1.53830e7			0.663955			0.331978	+	0.943287i	$0.392284\pi$
$884$	−4.86821e6	−	8.43199e6i	−0.209526	−	0.362910i
$885$	−2.69778e7	+	1.03654e7i	−1.15784	+	0.444864i
$886$	1.32027e7	−	2.28677e7i	0.565039	−	0.978675i
$887$	8.93554e6	−	1.54768e7i	0.381340	−	0.660500i	−0.609914	−	0.792467i	$-0.708796\pi$
$887$	8.93554e6	−	1.54768e7i	0.381340	−	0.660500i	0.991254	+	0.131968i	$0.0421295\pi$
$888$	−1.27494e6	+	8.06581e6i	−0.0542574	+	0.343254i
$889$	1.97022e7	+	3.41252e7i	0.836103	+	1.44817i
$890$	−3.35398e6			−0.141934
$891$	2.86891e6	−	2.76243e7i	0.121066	−	1.16573i
$892$	1.41627e7			0.595983
$893$	1.71880e7	+	2.97705e7i	0.721267	+	1.24927i
$894$	2.71794e6	−	1.71948e7i	0.113735	−	0.719536i
$895$	1.06501e7	−	1.84466e7i	0.444424	−	0.769766i
$896$	1.66561e6	−	2.88492e6i	0.0693112	−	0.120050i
$897$	3.36128e6	−	1.29147e6i	0.139484	−	0.0535923i
$898$	1.10462e7	+	1.91326e7i	0.457112	+	0.791741i
$899$	2.75385e6			0.113643
$900$	5.15638e6	+	1.67189e6i	0.212197	+	0.0688019i
$901$	−6.79137e6			−0.278705
$902$	−1.64784e7	−	2.85415e7i	−0.674372	−	1.16805i
$903$	5.63463e7	+	4.55995e7i	2.29957	+	1.86097i
$904$	14297.7	−	24764.3i	0.000581894	−	0.00100787i
$905$	5.94572e6	−	1.02983e7i	0.241314	−	0.417969i
$906$	1.38516e6	+	1.12097e6i	0.0560636	+	0.0453707i
$907$	2.54251e6	+	4.40375e6i	0.102623	+	0.177748i	0.912764	−	0.408486i	$-0.133943\pi$
$907$	2.54251e6	+	4.40375e6i	0.102623	+	0.177748i	−0.810142	+	0.586234i	$0.800610\pi$
$908$	5.09014e6			0.204887
$909$	2.88311e6	+	1.35229e7i	0.115732	+	0.542824i
$910$	−1.63427e7			−0.654215
$911$	2.52606e6	+	4.37526e6i	0.100843	+	0.174666i	0.912032	−	0.410118i	$-0.134513\pi$
$911$	2.52606e6	+	4.37526e6i	0.100843	+	0.174666i	−0.811189	+	0.584784i	$0.801179\pi$
$912$	7.37185e6	−	2.83240e6i	0.293487	−	0.112763i
$913$	1.21882e7	−	2.11107e7i	0.483910	−	0.838156i
$914$	−2.82687e6	+	4.89628e6i	−0.111928	+	0.193866i
$915$	−422059.	+	2.67012e6i	−0.0166656	+	0.105433i
$916$	−3.95095e6	−	6.84324e6i	−0.155583	−	0.269478i
$917$	−1.95342e7			−0.767136
$918$	−1.90623e7	+	1.01673e6i	−0.746566	+	0.0398199i
$919$	−3.46731e7			−1.35426			−0.677132	−	0.735861i	$-0.736777\pi$
$919$	−3.46731e7			−1.35426			−0.677132	+	0.735861i	$0.736777\pi$
$920$	−636675.	−	1.10275e6i	−0.0247998	−	0.0429545i
$921$	5.49120e6	−	3.47395e7i	0.213313	−	1.34951i
$922$	−1.70166e7	+	2.94737e7i	−0.659244	+	1.14184i
$923$	−527537.	+	913720.i	−0.0203821	+	0.0353028i
$924$	−2.22646e7	+	8.55447e6i	−0.857896	+	0.329620i
$925$	5.70583e6	+	9.88279e6i	0.219263	+	0.379774i
$926$	1.63262e7			0.625687
$927$	−3.55571e7	+	3.20556e7i	−1.35902	+	1.22519i
$928$	−1.18835e6			−0.0452976
$929$	8.00390e6	+	1.38632e7i	0.304272	+	0.527015i	0.977099	−	0.212785i	$-0.0682534\pi$
$929$	8.00390e6	+	1.38632e7i	0.304272	+	0.527015i	−0.672827	+	0.739800i	$0.734920\pi$
$930$	4.78513e6	+	3.87248e6i	0.181421	+	0.146819i
$931$	−2.42743e7	+	4.20444e7i	−0.917852	+	1.58977i
$932$	−9.29508e6	+	1.60996e7i	−0.350521	+	0.607120i
$933$	−2.17435e7	−	1.75964e7i	−0.817758	−	0.661789i
$934$	1.07648e7	+	1.86451e7i	0.403774	+	0.699356i
$935$	2.46521e7			0.922199
$936$	5.57924e6	−	5.02982e6i	0.208154	−	0.187656i
$937$	−1.90843e7			−0.710112			−0.355056	−	0.934845i	$-0.615538\pi$
$937$	−1.90843e7			−0.710112			−0.355056	+	0.934845i	$0.615538\pi$
$938$	999091.	+	1.73048e6i	0.0370764	+	0.0642183i
$939$	−8.20392e6	+	3.15210e6i	−0.303639	+	0.116664i
$940$	5.78143e6	−	1.00137e7i	0.213410	−	0.369637i
$941$	2.57109e7	−	4.45326e7i	0.946550	−	1.63947i	0.193933	−	0.981015i	$-0.437876\pi$
$941$	2.57109e7	−	4.45326e7i	0.946550	−	1.63947i	0.752617	−	0.658458i	$-0.228791\pi$
$942$	1.20964e6	−	7.65270e6i	0.0444151	−	0.280988i
$943$	−4.18882e6	−	7.25526e6i	−0.153396	−	0.265689i
$944$	−1.14083e7			−0.416668
$945$	−1.45202e7	+	2.85629e7i	−0.528923	+	1.04045i
$946$	4.30265e7			1.56318
$947$	2.11813e7	+	3.66871e7i	0.767498	+	1.32935i	0.938916	+	0.344147i	$0.111832\pi$
$947$	2.11813e7	+	3.66871e7i	0.767498	+	1.32935i	−0.171418	+	0.985198i	$0.554835\pi$
$948$	1.96778e6	−	1.24490e7i	0.0711141	−	0.449896i
$949$	−733535.	+	1.27052e6i	−0.0264396	+	0.0457948i
$950$	5.51808e6	−	9.55760e6i	0.198372	−	0.343590i
$951$	−4.63179e7	+	1.77962e7i	−1.66072	+	0.638081i
$952$	8.19701e6	+	1.41976e7i	0.293132	+	0.507719i
$953$	−3.48928e7			−1.24452			−0.622262	−	0.782809i	$-0.713786\pi$
$953$	−3.48928e7			−1.24452			−0.622262	+	0.782809i	$0.713786\pi$
$954$	−1.09255e6	−	5.12447e6i	−0.0388660	−	0.182296i
$955$	1.54980e6			0.0549880
$956$	9.26821e6	+	1.60530e7i	0.327983	+	0.568083i
$957$	6.61405e6	+	5.35257e6i	0.233446	+	0.188922i
$958$	1.71661e7	−	2.97326e7i	0.604308	−	1.04669i
$959$	2.36033e7	−	4.08821e7i	0.828755	−	1.43545i
$960$	−2.06489e6	−	1.67106e6i	−0.0723135	−	0.0585214i
$961$	1.14990e7	+	1.99169e7i	0.401655	+	0.695686i
$962$	1.58140e7			0.550939
$963$	5.42804e6	+	1.75997e6i	0.188615	+	0.0611560i
$964$	−1.31378e7			−0.455335
$965$	−1.20389e7	−	2.08521e7i	−0.416170	−	0.720827i
$966$	−5.65967e6	+	2.17455e6i	−0.195141	+	0.0749767i
$967$	−3.66580e6	+	6.34935e6i	−0.126067	+	0.218355i	−0.922150	−	0.386833i	$-0.873569\pi$
$967$	−3.66580e6	+	6.34935e6i	−0.126067	+	0.218355i	0.796082	+	0.605188i	$0.206902\pi$
$968$	−1.92527e6	+	3.33467e6i	−0.0660396	+	0.114384i
$969$	−6.06796e6	+	3.83884e7i	−0.207603	+	1.31338i
$970$	−6.69213e6	−	1.15911e7i	−0.228368	−	0.395545i
$971$	3.45114e6			0.117467			0.0587334	−	0.998274i	$-0.481294\pi$
$971$	3.45114e6			0.117467			0.0587334	+	0.998274i	$0.481294\pi$
$972$	−3.83379e6	−	1.42200e7i	−0.130156	−	0.482762i
$973$	3.26469e7			1.10550
$974$	7.93340e6	+	1.37410e7i	0.267955	+	0.464112i
$975$	1.63896e6	−	1.03688e7i	0.0552151	−	0.349313i
$976$	−533547.	+	924130.i	−0.0179287	+	0.0310534i
$977$	1.14779e7	−	1.98803e7i	0.384704	−	0.666326i	−0.607024	−	0.794683i	$-0.707637\pi$
$977$	1.14779e7	−	1.98803e7i	0.384704	−	0.666326i	0.991728	+	0.128357i	$0.0409704\pi$
$978$	9.53943e6	−	3.66523e6i	0.318915	−	0.122533i
$979$	4.73975e6	+	8.20949e6i	0.158052	+	0.273753i
$980$	1.63300e7			0.543153
$981$	2.74031e7	+	8.88509e6i	0.909133	+	0.294774i
$982$	2.30564e7			0.762978
$983$	−2.52879e7	−	4.38000e7i	−0.834698	−	1.44574i	−0.894276	−	0.447516i	$-0.852309\pi$
$983$	−2.52879e7	−	4.38000e7i	−0.834698	−	1.44574i	0.0595772	−	0.998224i	$-0.481025\pi$
$984$	−1.35854e7	−	1.09943e7i	−0.447285	−	0.361976i
$985$	−4.87556e6	+	8.44471e6i	−0.160116	+	0.277328i
$986$	2.92413e6	−	5.06474e6i	0.0957866	−	0.165907i
$987$	−4.27976e7	−	3.46349e7i	−1.39838	−	1.13167i
$988$	−7.64681e6	−	1.32447e7i	−0.249223	−	0.431667i
$989$	1.09373e7			0.355567
$990$	3.96586e6	+	1.86014e7i	0.128603	+	0.603194i
$991$	−3.58604e7			−1.15993			−0.579964	−	0.814642i	$-0.696933\pi$
$991$	−3.58604e7			−1.15993			−0.579964	+	0.814642i	$0.696933\pi$
$992$	1.21497e6	+	2.10439e6i	0.0392001	+	0.0678965i
$993$	−109498.	+	42071.2i	−0.00352398	+	0.00135398i
$994$	888257.	−	1.53851e6i	0.0285150	−	0.0493894i
$995$	−4.17174e6	+	7.22567e6i	−0.133586	+	0.231377i
$996$	2.01823e6	−	1.27681e7i	0.0644647	−	0.407830i
$997$	1.75536e7	+	3.04037e7i	0.559279	+	0.968699i	0.997557	+	0.0698599i	$0.0222552\pi$
$997$	1.75536e7	+	3.04037e7i	0.559279	+	0.968699i	−0.438278	+	0.898839i	$0.644411\pi$
$998$	−1.85602e7			−0.589872
$999$	1.40504e7	−	2.76388e7i	0.445426	−	0.876204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.6.c.b.13.2	yes	6
3.2	odd	2		54.6.c.b.37.2		6
4.3	odd	2		144.6.i.b.49.2		6
9.2	odd	6		54.6.c.b.19.2		6
9.4	even	3		162.6.a.j.1.2		3
9.5	odd	6		162.6.a.i.1.2		3
9.7	even	3	inner	18.6.c.b.7.2	✓	6
12.11	even	2		432.6.i.b.145.2		6
36.7	odd	6		144.6.i.b.97.2		6
36.11	even	6		432.6.i.b.289.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.c.b.7.2	✓	6	9.7	even	3	inner
18.6.c.b.13.2	yes	6	1.1	even	1	trivial
54.6.c.b.19.2		6	9.2	odd	6
54.6.c.b.37.2		6	3.2	odd	2
144.6.i.b.49.2		6	4.3	odd	2
144.6.i.b.97.2		6	36.7	odd	6
162.6.a.i.1.2		3	9.5	odd	6
162.6.a.j.1.2		3	9.4	even	3
432.6.i.b.145.2		6	12.11	even	2
432.6.i.b.289.2		6	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	18.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 3.46410i) q^{2} +(-2.43381 + 15.3973i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-20.8014 + 36.0292i) q^{5} +(58.2054 - 22.3636i) q^{6} +(101.661 + 176.082i) q^{7} +64.0000 q^{8} +(-231.153 - 74.9483i) q^{9} +166.412 q^{10} +(-235.168 - 407.323i) q^{11} +(-193.881 - 156.902i) q^{12} +(-241.506 + 418.300i) q^{13} +(406.643 - 704.326i) q^{14} +(-504.125 - 407.974i) q^{15} +(-128.000 - 221.703i) q^{16} +1259.86 q^{17} +(202.678 + 950.634i) q^{18} +1978.94 q^{19} +(-332.823 - 576.466i) q^{20} +(-2958.60 + 1136.75i) q^{21} +(-940.672 + 1629.29i) q^{22} +(-239.119 + 414.166i) q^{23} +(-155.764 + 985.427i) q^{24} +(697.100 + 1207.41i) q^{25} +1932.04 q^{26} +(1716.58 - 3376.72i) q^{27} -3253.14 q^{28} +(580.249 + 1005.02i) q^{29} +(-405.015 + 2562.29i) q^{30} +(1186.50 - 2055.07i) q^{31} +(-512.000 + 886.810i) q^{32} +(6844.02 - 2629.60i) q^{33} +(-2519.72 - 4364.28i) q^{34} -8458.76 q^{35} +(2887.74 - 2603.37i) q^{36} +8185.10 q^{37} +(-3957.89 - 6855.26i) q^{38} +(-5852.91 - 4736.60i) q^{39} +(-1331.29 + 2305.87i) q^{40} +(-8758.87 + 15170.8i) q^{41} +(9855.02 + 7975.40i) q^{42} +(-11435.0 - 19806.1i) q^{43} +7525.37 q^{44} +(7508.64 - 6769.22i) q^{45} +1912.95 q^{46} +(8685.43 + 15043.6i) q^{47} +(3725.15 - 1431.27i) q^{48} +(-12266.3 + 21245.9i) q^{49} +(2788.40 - 4829.65i) q^{50} +(-3066.26 + 19398.4i) q^{51} +(-3864.09 - 6692.80i) q^{52} -5390.58 q^{53} +(-15130.5 + 807.021i) q^{54} +19567.3 q^{55} +(6506.29 + 11269.2i) q^{56} +(-4816.38 + 30470.4i) q^{57} +(2321.00 - 4020.09i) q^{58} +(22281.8 - 38593.2i) q^{59} +(9686.05 - 3721.56i) q^{60} +(-2084.17 - 3609.88i) q^{61} -9491.97 q^{62} +(-10302.2 - 48321.1i) q^{63} +4096.00 q^{64} +(-10047.3 - 17402.5i) q^{65} +(-22797.3 - 18449.2i) q^{66} +(-1228.46 + 2127.76i) q^{67} +(-10078.9 + 17457.1i) q^{68} +(-5795.07 - 4689.79i) q^{69} +(16917.5 + 29302.0i) q^{70} +2184.37 q^{71} +(-14793.8 - 4796.69i) q^{72} +3037.34 q^{73} +(-16370.2 - 28354.0i) q^{74} +(-20287.5 + 7794.83i) q^{75} +(-15831.5 + 27421.0i) q^{76} +(47814.7 - 82817.5i) q^{77} +(-4702.24 + 29748.3i) q^{78} +(25266.2 + 43762.3i) q^{79} +10650.3 q^{80} +(47814.5 + 34649.1i) q^{81} +70070.9 q^{82} +(25913.9 + 44884.2i) q^{83} +(7917.55 - 50089.6i) q^{84} +(-26206.9 + 45391.7i) q^{85} +(-45740.1 + 79224.3i) q^{86} +(-16886.8 + 6488.23i) q^{87} +(-15050.7 - 26068.7i) q^{88} -20154.7 q^{89} +(-38466.5 - 12472.3i) q^{90} -98206.5 q^{91} +(-3825.91 - 6626.66i) q^{92} +(28754.8 + 23270.5i) q^{93} +(34741.7 - 60174.4i) q^{94} +(-41164.9 + 71299.6i) q^{95} +(-12408.4 - 10041.7i) q^{96} +(-40214.4 - 69653.3i) q^{97} +98130.4 q^{98} +(23831.7 + 111779. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12 q^{2} + 9 q^{3} - 48 q^{4} - 54 q^{5} - 12 q^{6} - 132 q^{7} + 384 q^{8} - 177 q^{9} + 432 q^{10} - 315 q^{11} - 96 q^{12} - 744 q^{13} - 528 q^{14} + 2286 q^{15} - 768 q^{16} + 2898 q^{17} + 1056 q^{18}+ \cdots + 282168 q^{99}+O(q^{100}) \) 6 * q - 12 * q^2 + 9 * q^3 - 48 * q^4 - 54 * q^5 - 12 * q^6 - 132 * q^7 + 384 * q^8 - 177 * q^9 + 432 * q^10 - 315 * q^11 - 96 * q^12 - 744 * q^13 - 528 * q^14 + 2286 * q^15 - 768 * q^16 + 2898 * q^17 + 1056 * q^18 + 2262 * q^19 - 864 * q^20 - 11076 * q^21 - 1260 * q^22 - 3168 * q^23 + 576 * q^24 - 2883 * q^25 + 5952 * q^26 + 18144 * q^27 + 4224 * q^28 - 5148 * q^29 - 14400 * q^30 - 8610 * q^31 - 3072 * q^32 + 17469 * q^33 - 5796 * q^34 + 2700 * q^35 - 1392 * q^36 + 39936 * q^37 - 4524 * q^38 - 49026 * q^39 - 3456 * q^40 + 5049 * q^41 + 41352 * q^42 - 31389 * q^43 + 10080 * q^44 + 2538 * q^45 + 25344 * q^46 + 12924 * q^47 - 768 * q^48 - 52857 * q^49 - 11532 * q^50 + 36837 * q^51 - 11904 * q^52 - 96048 * q^53 - 71892 * q^54 + 126252 * q^55 - 8448 * q^56 - 17469 * q^57 - 20592 * q^58 + 62955 * q^59 + 21024 * q^60 - 75966 * q^61 + 68880 * q^62 + 49578 * q^63 + 24576 * q^64 + 108702 * q^65 + 2952 * q^66 - 32991 * q^67 - 23184 * q^68 - 29250 * q^69 - 5400 * q^70 - 129672 * q^71 - 11328 * q^72 - 8466 * q^73 - 79872 * q^74 - 105483 * q^75 - 18096 * q^76 + 88740 * q^77 + 171720 * q^78 + 89202 * q^79 + 27648 * q^80 + 123435 * q^81 - 40392 * q^82 + 32634 * q^83 + 11808 * q^84 + 71388 * q^85 - 125556 * q^86 - 151524 * q^87 - 20160 * q^88 + 66132 * q^89 - 263088 * q^90 - 301836 * q^91 - 50688 * q^92 + 57678 * q^93 + 51696 * q^94 - 82944 * q^95 - 6144 * q^96 + 46245 * q^97 + 422856 * q^98 + 282168 * q^99

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